Term used in roleplaying game circles for a player - often literally the DM's girlfriend, sometimes a younger family member - who is getting special treatment from the gamemaster due to an out-of game personal relationship, specifically because the GM either wants to curry favor with them or is afraid of incurring their ire. This is often at the expense of other players, who showed up at the table to participate equally, but have somehow ended up playing sidekicks to the Dungeon Master's Girlfriend.
This trope is much older than, and not limited to gaming situations, though. Before there were RPGs, it was a situation that would arise in theatre, film, and TV — the director would give his girlfriend a large or important role, or a producer would insist that his current girlfriend be given a part as a condition for his backing. In most cases, she is not competent enough to handle the role; in some, she's not competent at all.
This is not a trope about someone that does something only because their significant other is doing it, though the situations do often overlap (sometimes the favoritism is in place to go easy on this new player).
In case of roleplay, the girlfriend or sibling might actually have an advantage by knowing the DM better than the other players without any favoritism coming into play.
Compare Nepotism. This person may be regarded as something of a Yoko Oh No, especially in the case of film and music, and also may result in the Love Makes You Uncreative trope being invoked.
The Godfather had Francis Ford Coppola's daughter Sofia play Michael Corleone's daughter Mary. It didn't go well (fortunately, she became a quite talented director in her own right instead of pursuing a career in acting).
Underworld has Kate Beckinsale, who met the director on set and is now married to him. Guess who all the action in 4 films centers on.
In a very similar vein, Milla Jovovich in the Resident Evil film series met the director on set and they are now married. Might explain some of her telekinesis, super strength, replication and Healing Factor when the video games are mostly about Badass Normal people fighting zombies and mutant creatures.
Double Subverted in The Fifth Element. Luc Besson wanted his girlfriend to play Diva Plavalaguna, but she initially refused. It was only when the actress they hired backed out that she relented.
The Rocketeer used it in-universe. Jenny has a bit part in a movie, and complains to some extras that the (very hammy) leading lady only got the job because she's the producer's niece.
Helen Chadwick's classic role as the interfering lead singer's girlfriend in This Is Spinal Tap. This has to be the portmanteau example of every famous time a band member's girlfriend has interfered in the band...
On The Big Bang Theory the guys plan on having a no girlfriends, weekend gaming marathon but Howard's fiancée Bernadette ends up tagging along. She's a useless addition to their fighting party, saying "pew, pew" instead of actually hitting the keys to shoot and concentrating solely on healing her fiancée's character (when she's supposed to be the group healer). But of course, they all put up with it and don't kick the both of them out because well, for one thing it'd be mean (and she meant well). Oddly enough it's mostly averted by Penny; when she bothers to join in on Halo Night she's actually a kick ass gamer in her own right.
Frasier: "Where Every Bloke Knows Your Name", used and subverted at the same time.
In one episode of The Red Skelton Show, Clem Kadiddlehopper strikes oil. Using his new found riches he acquires a television station putting on a talent show, which he insists his girlfriend Daisy will be the winner of even though she was not planned to be a contestant. The producers of the show walk forcing Clem to try to run the thing himself.
One very early Dragon magazine short story (by Roger Moore... no, not him) used this trope in-character, when a tavernful of male adventurers were bragging of their power, achievements, and connections to still-greater beings. A woman at a private table kept snickering at their boasts, until they got fed up and confronted her with sexist remarks. She sneered at their petty claims, threw back her cloak to expose her magnificent armor, weapons, and other bling, and proclaimed: "My husband is the Dungeon Master." The boasters all looked up, anticipating a vengeful bolt from the blue, then very quickly evacuated the tavern when they realized no such retribution was coming.
Inverted in the sequel to the famous Dead Alewives' Dungeons & Dragons sketch. One of the players brings his girlfriend and the DM treats her very passive-aggressively, allowing her to play but not explaining the rules or what's going on in the session, then places her character in a concrete room with no exits. The character has a spell that can be used to escape, but the player isn't informed of this, and leaves in a huff to the DM's evident satisfaction.
Built into the rules of the D20 version of Munchkin is a feat called "Shagging the DM". It has only one prerequisite, and it's in the title. It allows you to reroll one roll every 30 minutes. (The feat's description also points out that if you qualify for it, you probably don't need it.)
Gabe of Penny Arcadegives this to Vin Diesel, not because of a relationship, but because he is abjectly terrified of Vin Diesel.
Gabe: The skeleton lashes out at you, Vin, for... [Vin glares] ...zero damage! He missed! Again. And then... he died. So you get a million XP. And all the gold. And you win the whole game, forever.
In Darths & Droids, when Ben's sister Sally is first brought in, she kinda gets this treatment, with the DM having to accede to her alterations to his game to keep her from crying. It helps that the players consider her ideas cooler than his.
Variation with Asenath Summerisle in The Binder of Shame; she's introduced as Deviant Boy's girlfriend while he's running a game. She herself is an okay gamer and ends up getting along fine with the guys, but he warps the entire game to revolve around her Mary Sue character; "She got to play hero while the rest of us swam through raw sewage being chased by vaguely alien sex slavers."
Unfortunately, a very real problem IRL, especially when a dungeonmaster's significant other is playing the game for the first time.
Another problem is that people may perceive it happening when it isn't, or the Dungeon Master isn't sure how much slack to give to their significant other's character and they are instead overly harsh. Prospective D Ms need to be careful to disassociate your players from their characters since favoritism will breed resentment in all parties, including (and even especially) the one receiving favor since they can easily find it condescending. If unsure, just ask the other players privately if they think you are playing favorites and see what they have to say.