A Stock Pose where a character, usually a guy, proclaims something he is determined to accomplish, or to express pride, where he holds up his fist to his shoulder, palm facing inward, and the fist might even shake a little.
The girly version of this has the fist bent outwards while the fist still faces inward, a variation is to pump one hand all the way up with one hand doing a downward pump as if stretching.
This is called "Guts Pose" (Gatsu Pozu) in Wasei Eigo, which was apparently coined by Guts Ishimatsu.
Being Hot-Blooded or a Genki Girl will of course make this pose more likely. It can be accompanied by shouting Big "YES!".
This is so common, that it's spoofed as often as it's played straight. Some parodies even have the guy crying Manly Tears of pride.
Do not confuse with the Handshake Substitute "Fist Bump".
Compare Fist of Rage, Angry Fist-Shake or Milking the Giant Cow.
In Fate/stay night, Shirou does a subdued version of this, explaining that it's right and proper for people who are mortally wounded to die of their wounds, and thus, that it's okay for him to relinquish the power that had kept him alive when he should have died many times over, for the sake of protecting the one he loves.
In the Dragon Half OVA, Princess Vina slowly curls her fingers into one of these when she hears of the plan to get her self-proclaimed rival Mink into the Brutal Killer Martial Arts Tournament — Vina chooses to join as well in order to be the one to eliminate Mink.
Pokémon: The anime does this a lot when the main characters are excited after catching a pokemon, landing a strong hit with an attack, or they win a pokemon battle.
Film — Animated
Mega Mind: When Megamind is in disguise, trying to train Titan, he does this.
After the Klingon Bird-of-Prey is destroyed, Data (who is under the influence of the emotion chip) does this gesture and gives a Big "YES!".
There's an extra in the background who also does a fist pump just before Data does it, then (out of universe) tries to hide the fact that he did it in order to not ruin Data's moment.
Used in Bruce Almighty, when Bruce ends his disastrous Maid of the Mist report by saying, "Back to you, fuckers!" In a cable TV edit anyway, because on VHS and DVD, Bruce gives us the finger.
The Breakfast Club fades out on Bender with his fist in the air, triumphant over the events of the day.
In Hot Shots!: Part Deux, an Iraqi soldier does this after he and the protagonist manage to kill the Energizer Bunny.
Animorphs: When Cassie rescues Ketran from the Yeerk pool, she sees one of the Controllers shaking his fist in what looks like impotent rage. Except she knows that he's a mole, so he's really cheering her on.
In the Aunt Dimity series: After the successful confrontation with the Bowenists and their guru near the end of Aunt Dimity and the Village Witch, Bree Pym does one of these (with her arm out of her car window) as she drives away from Fairworth House.
Live Action TV
The X-Files, "Arcadia": Agent Mulder wants to prove his theory on the case of the week, which involves people obsessing with housing rules and neatness. He carries out a very kitschy pink plastic flamingo and puts it up in the front yard. He looks around confidently and pumps his both fists, and says: "Bring it on!"
Murphy does it in an episode of Murphy Brown while expressing enthusiasm for getting a scoop interview.
On Arrow, Oliver and Diggle are impatiently waiting for Felicity to hack a bad guy's computer. "Just so you know, when I finish, I'll put my fist in the air and say 'Yeah!'". Later, when she finally succeeds, she does exactly that.
The Lizzie Bennet Diaries: According to Lizzie, this is what Mrs Bennet did at Ellen Gibson's wedding when she was enjoying her success as a matchmaker when her daughter Jane and Bing hit it off, dancing together song after song. Let's hope Lizzie meant it metaphorically.
Lizzie: Then [I was] watching mom pump her fist so that everyone in the world knew of her unbridled success.
Regular Show: Parodies this in the episode "Fist Pump". Mordecai and Rigby want to get concert tickets for a band of the same name. They do this pose many times throughout the episode while shouting "Fiiist Puuummmp".