A character with a guilty conscience reacts to the appearance of an authority figure with a cry of "Wait! I can explain!" and launches into an explanation of how whatever-it-was wasn't their fault.
Often, it turns out that the authority figure really wanted to talk to them about something else, and wouldn't even have known about whatever-it-was if they hadn't tried to explain.
The next step in the evolution of this trope is also common: a parent will confront their kid in a vague way, and the kid will confess to whatever he or she has done. The parent either knew the kid was up to something, but had little idea of what the specifics were; or, the parent was just making a routine surprise inspection.
Alternately, a phrase spoken by someone whose masquerade's about to be blown who's about to make with some quick Clark Kenting to protect the secret.
A Discredited Trope as the line is rarely played straight nowadays. And considered the number of times its been parodied/subverted, it's well on its way to be a Dead Horse Trope. As such, a common subversion is for the character in question to deliver this line... then resignedly admit that no, actually they can't explain it.
Often caused by the situation being Not What It Looks Like. See also the cousin Trope Noodle Incident.
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Anime and Manga
Rika in Digimon Tamers saying this in episode 24 when her grandmother gets the chance of seeing Renamon.
Mana in DokiDoki! Precure said this when her friend, Alice, caught her and Rikka's transformation.
Higurashi: When They Cry: Keiichi to Satoko, during the Curse Killing Arc. Satoko arrives back on the scene just in time to see Keiichi holding a bloody axe, with Rika's mutilated body on the ground next to him. Understandably, she's a little more than distressed at this. Keiichi proceeds to chase her and yell variations of this and Not What It Looks Like at her. He really didn't do it. He was just holding the Idiot Ball at the time.
Steele: You guys weren't there, so you don't—wait a minute, guys! Wait just a second...please!
Ultimate Avengers has Bruce Banner's plot of using the Super Soldier Serum on himself so he could control the Hulk has been discovered so he gives out this explanation before being pinned down by Nick Fury.
Film - Live-Action
Subverted heavily in The Usual Suspects, where Verbal's attempts to evade giving information to the police turn out to be an elaborate strategy to get the police to believe him when he actually does provide (wrong) information.
Subverted in Iron Man when Pepper walks in on Tony apparently being molested by robots:
Stanley Ipkiss: Wait, I can explain everything! Lt. Kellaway: Oh yeah? You can explain everything? [gets the rubber mask from the jacket] Explain this. Stanley Ipkiss: Um...
It should be noted, that was a fake mask the Big Bad slipped into Stanley's jacket to make him look like a liar.
The Departed when Maddy, the psychiatrist, finds out Sullivan working for Costello.
Maddy: You know, I thought I was the liar.
Sullivan: Hey, I can explain that!
Played for laughs in The Blues Brothers where the 'explanation' turns out to be a series of increasingly unlikely excuses. Amazingly enough they do the job and let the brothers make their escape.
The 1982 and 1999 film versions of Annie include the scene from the musical where Miss Hannigan defends herself regarding Annie's escape attempt, thinking that Grace Farrell came to the orphanage to investigate that incident.
Making Money features Moist von Lipwig's first words to Lord Vetinari when he has been summoned as "look, I can explain." Vetinari's actually summoned him for something else entirely, but Moist does have to spend some time why there were mongooses in the posting boxes. (Someone had come up with the brilliant idea of Summon Bigger Fish to take care of snakes, who were introduced to eat the toads, who were introduced to eat the snails, who were eating the glue on the postage stamps.)
In the Hank the Cowdog book "The Case of the Measled Cowboy", Hank begins to rehearse his explanation to the woman of the house, Sally May, for the tremendous mess that he and her son made in her absence. Subverted in that he admits he can't get any farther than "I can explain."
Lex Luthor, in an attempt to convince a female friend that she deserves better, got her to a nightclub, where she found the man she is engaged with when he is supposed to be on a business trip. The guy says the line repeatedly. To quote a reviewer, "If you are just going to say that, it is clear that you can't explain s***."
When Chloe and Clark are both not themselves, they do some intense making out right under Lana's nose. When Chloe strips Clark, the red kryptonite is removed and he is back to normal. He says this to Lana who slams the door in his face after Not What It Looks Like. He can't explain anyway as he must save Chloe before she get herself killed as some parasite makes her dangerously impulsive, and Clark can't tell Lana about the red kryptonite anyway.
Lana once says this when Lex finds out she stole his car. There is absolutely nothing she could explain, really.
Jimmy says this when Chloe, who is at the time his girlfriend, walk in on Kara and him alone but not doing anything suspicious. Chloe's paranoia is somewhat justified given her meteor infection.
Clark tells this to Lois when he "accidentally" left her in the rain for three hours.
And again in "Echo" when he didn't show up for a date.
A priest disturbs Sam as he's performing a seance in the church basement.
Sam: I can explain… actually, no I can't.
A couple of Hunters discover Sam's role in starting the Apocalypse and declare they're going to blow his head off. Sam says he can explain, then flounders because he is in fact guilty as hell. So they kill him. Again.
Much British humor (Fawlty Towers, Mr. Bean, and Jeeves and Wooster being prime examples) is based on this sort of thing, although the three examples are set about it in different ways. Basil Fawlty comes up with an explanation that is even more unbelievable than the truth, Bean just pretends nothing is happening, and Bertie Wooster gets too nervous to explain.
General: Can you explain to me why several witnesses put you people at a restaurant in town last night? Daniel (interrupting Jack): Sir, I can explain everything! (Pauses) No, I can't.
From BlackAdder Goes Forth, Blackadder assuming that his commanding officer has realized his glamorous showgirl is actually a "strapping six-footer from the rough end of the trenches":
Blackadder: I can explain everything, sir! Melchett: Can you, Blackadder? Can you? Blackadder: Well...no, sir.
And of course, he thinks Blackadder is saying he can't explain "the mystery of love" and he remains blissfully unaware that the woman he loves is one of his underlings.
Another one earlier in the same series; Blackadder has been repreived from his death sentence by George's uncle, and then learnt that George and Baldrick got drunk and never actually asked his uncle to do so.
Baldrick: I think I can explain, sir. Blackadder: Can you, Baldrick? (Beat) Baldrick: No.
The earlier Blackadder II had a similar gag where Blackadder is entertaining his fiercely Puritanical aunt and uncle while simultaneously holding a drinking competition. Things seem to be going well, until one of the drunks (dressed as a monk) bursts into the room, vomits in the fireplace, and leaves, saying "Great booze-up, Edmund!" When asked if he can explain, Blackadder spends the next minute staring into space and working his jaw as he tries to come up with an explanation, then finally says "...Yes I can."
Incidentally, the man really was a monk, although one of extremely ill repute. Considering that puritans couldn't stand monastical system, that probably didn't do Edmund any favours, either.
Later in the same episode Blackadder returns to the room, completely 'faced, wearing a cardinal's hat, fake breasts and a feather up his bum. When his Aunt demands he explains, he just pauses a second and replies "....I can't. Not just like that."
Lampshaded when Ted is caught with a stolen whistle and attempts to explain everything with a hastily-improvised sob story about a crippled boy attempting to train a horse to win the Grand National. He stops halfway through when Dougal reveals that they found out the real culprit while Ted was out of the room.
Played entirely straight, however, in "Are You Right There, Father Ted?", featuring the collector of Nazi memorabilia who has left his collection to Ted in his will for various farcical reasons - a collection Mrs Doyle has put up in the house, believing it to be the expected delivery of new furniture - just before Ted returns from the pub with the inhabitants of the island's Chinatown. Uses the seemingly common "I can explain everything... Actually, no, I can't" delivery.
Subverted in Coupling when Susan accuses her ex Patrick of filming them in bed together and keeping the video. Patrick responds with "I can explain.....Yes I did".
Blurted by Nate in an episode of Leverage. When his ex-wife finds him after he came to Kiev when he heard she was in trouble, he speaks this line. It's also used in the first season finale when his ex-wife finds out that he was spying on her. Word of God says that he used the phrase a lot during their marriage.
The Drake & Josh pilot episode has this when the former caught the latter dressing up like a woman:
Drake: Oh my God!
Josh: I can explain!
Drake: Oh my God!
Josh: I can explain!
Community: Jeff when noticed by one of his former lawyer buddies, has to come up with an explanation on the spot.
Jeff: I can explain. I'm a teacher. Wait, that's worse than the truth. I'm a student.
Later in the same episode, Troy says it verbatim to a janitor who catches him in someone else's office. Then he plays for time by insisting "Let me explain!" to the still silent janitor, and then stands there awkwardly, unable to think of anything, until Annie comes in and chloroforms him.
Whenever Doña Florinda assumes Don Ramón did or tried to do something to her son, she won't listen to whatever explanation he's got to offer.
Also, Don Ramón once told his daughter Professor Jirafales was coming to visit him. Her immediate reaction was loudly pleading him not to believe anything Professor Jirafales says. Don Ramón asked her what he'd say and she realized she spoke too much.
Phoebe: Oh my God, you're getting a massage? You never let me massage you!
Monica: Phoebe, I can explain! You see...God, I gotta get better at lying.
NCIS had a scene where Tony was doing a horse impression and suddenly realized from everyone's expressions that Director Vance was right behind him:
Tony:(without daring to turn and look) I can explain, sir. Vance: Sit down, Doctornote He's accompanied by an NCIS psychiatrist, this should be good.
Calvin and Hobbes used this trope when Calvin's mother went for an interview with his teacher, Miss Wormwood. Calvin begins packing a suitcase to run away. When his mother comes back and tries to talk to him, she unknowingly Perp Sweats him and he panics as he tries to explain what he thinks Miss Wormwood told her:
Calvin's Mom: Calvin, I...
Calvin: Yike! You're home! I didn't even finish pack...that is...um...lies! Everything Miss Wormwood said about me was a lie! She just doesn't like me! She hates little boys! It's not my fault! I'm not to blame! She told you about the noodles, right? It wasn't me! Nobody saw me! I was framed! I wouldn't do anything like that! I'm innocent, I tell you!
Calvin's Mom: What noodles?
Calvin: Oh! Uh...noodles? Ha ha...you must have heard wrong. I didn't say noodles.
In one strip Peter punches a guy at school for making a joke about Denise and is told his parents will be called:
Peter (worried): Hi.
Andy: Peter, the school called me today.
Peter: Look, I know what you're going to say. Fighting is wrong. I know that. It was a momentary lapse. It won't happen again. I'll have to serve detention, but Mr. Krimpshaw says he may not put it on my permanent record. I'm sorry, I'm sorry, I'm sorry. I was an idiot, all right?!
Andy: They called to say someone found your wallet.
Peter (thinking): "Was" nothing.
Andy: Now, then. What's all this about a fight?...
Parodied in Nebulous, where Nebulous's underling's try to explain their attempted Dying Declaration of Love, but Nebulous simply shrugs the explanation off, saying "if you got drunk and indulged in foreplay, I'm sure you had a damn good reason."
In practically every episode of Navy Lark, CPO Pertwee is caught out ... exclaims, "I can explain!" ... and often does.
Annie, the musical: Shortly after Annie's attempt to escape from Miss Hannigan's orphanage, a woman arrives and announces that she has been sent to talk to Miss Hannigan by the orphanage's board of directors. Miss Hannigan is in full self-justifying flight before the woman has a chance to explain that actually she's just come to see about borrowing one of the orphans.
The trailer for World of Warcraft''s raid instance, Ulduar, has Rhonin meeting the human king Varian. However, Rhonin had also invited Thrall and Garrosh to meet with him. Problem is, Thrall and Garrosh show up earlier than expected and when the Varian and Thrall see each other, Rhonin reacts this way. He sounded suspiciously as if he was caught cheating on his wife.
In Too Much Information, when Ace (who occasionally live up to his name) is making out with a strappin' Scottish lass on the doorstep, and her grandmother walks in on them, his quick "I can explain!" is answered by a dry "Be fun tae see ye try..." before the Cool Old Lady reveals that she's got no objections whatsoever.
Not Invented Here: Desmond and Owen are caught in the middle of a wooded area, in a motor home, wearing hazard suits, surrounded by cough medicine containers. Fortunately, Desmond's explanation is taken as truth.
Danny's response after the strange events of the Free the Frogs episode? "I can explain... actually, I really can't."
When his family (mostly Jazz) comments on his odd behavior, Danny's Response is "ITS A LIE, I'M NOTA GHOST!" Thankfully, Jazz just figured he'd gotten a girlfriend.
Twice in the episode "Prehibernation Week" of SpongeBob SquarePants, an ordinarily normal-looking fish is revealed to apparently wear Osh-Kosh overalls, a beanie, and a giant lollipop underneath his regular clothes (well, okay, the second time Sandy just ripped up a building from its foundation and revealed the fish in the kiddy clothes, but anyway). One short pause later, the fish responds with "Uhh, I can explain..."
American Dragon Jake Long: The Halloween Episode featured Jake having a Halloween party and inviting both humans and magical creatures. Unfortunately, it was just when the Dragon Council decided it was his turn to make a surprise inspection.
In the Aladdin: The Series episode "Dune Quixote", Aladdin finds himself kissing Sadira with Jasmine standing nearby. On impulse, he quickly starts to say he can explain before realizing that he can't explain. (Sadira had cast a spell on Aladdin that ended up going horribly wrong, trapping Aladdin in a bizarre fantasy, and only ending when he kissed Sadira, which Jasmine reluctantly allowed in order to get Aladdin back to normal.)
In Transformers Prime, Jack is caught violating his curfew by his mother, June, and tries to explain that he is really a contact for an alien race engaged in a war on Earth. June doesn't buy it. Later on, she's kidnapped by MECH and Airachnid, forcing Jack and Arcee to rescue her. As Jack is trying to free her, he says he can explain everything—then stops, and goes, "Wait, I already did."