A "Comfort Food" is a familiar food that a person eats because doing so relieves stress and anxiety and increases contentment and comfort (hence the name). It sparks happy memories, brings back feelings of security and safety, and thus can easily lift a person's mood.
Comfort food for most people tends to also be their favorite food, or the food they enjoyed the most while growing up. In his book A Cook's Tour, Celebrity Chef and Television Host Anthony Bourdain noted that, among big name chefs who specialize in fine cuisine at their restaurants, the most common type of answer to "If you were about to die and had time for one last meal, what would it be?" were meals like "my Grandmother's meat loaf" or "a nice hot ham-and-cheese sandwich" or "oreos and a tall glass of ice cold milk". Other common answers were things like "a Big Mac", "mint chocolate chip ice cream", "an entire bag of Lay's Barbecue chips", and "a chili dog".
In other words, Comfort Food.
Because corporations know a cash cow when they see it, there are entire restaurant chains devoted to serving you comfort food, like Bob Evans, Cracker Barrel, and Boston Market.
May overlap with Your Favorite. Heartbreak and Ice Cream is a common Sub Trope. See also I Need a Freaking Drink and Drowning My Sorrows.
Examples:
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Anime and Manga
One Pound Gospel: Kosaku starts pigging out after Sister Angela tells him that she can't spend any more time with him until he stops liking her as more than a friend.
Sorta used in Persona 4: The Animation when Aika offers the Rainy Day Special to Yu after Nanako's death. Yu is in such a depressed state that he actually eats it whole in few minutes. (Notice that this is a beef bowl that Yu and his friends have eaten before, and it's so... special that it's almost impossible to eat in less than 40 minutes.)
In Inukami! Youko's Trademark favorite food is Chocolate cake turns out her crush gave her some when he was much younger, he doesn't remember it but this act of kindness when stuck on a mountain and surrounded by dogs, turned her into a yandere for him
Film
In Constantine, after a jaunt into Hell for information, Constantine declares he needs to eat. It's unclear if this is to cope with the trauma or because he had used up a lot of calories in his psychic journey, but in the film it seems to be a little of both.
In Iron Man, the first thing Tony Stark asks for when he gets back to the safety of American soil after being held hostage by the Five Rings is for a Burger King Whopper. Product Placement, sure, but it's also not so hard to imagine someone like Tony Stark thinking of a Whopper as comfort food.
Tony's actual request is for "an American Cheeseburger," it is simply most likely , in universe, that the first oportuninty to buy one was at BK. Not that it wasn't product placement for us.
In Gotcha, after Anthony Edwards manages to return to West Berlin after a rather traumatic trip to the East, the first thing he does is go to West Berlin's McDonald's and order "an American cheeseburger, some American fries, and a nice, thick, American milkshake."
"Of course I'm not happy! Look at me, I'm a big fat slob. I've got bigger titties than you do. I've got more chins than a Chinese phonebook. I've not seen my willie in two years, which is long enough to declare it legally dead. (on the verge of tears) I can't stop eating. I eat because I'm unhappy, and I'm unhappy because I eat. It's a vicious cycle."
Keep in mind that his idea of Comfort Food includes human babies.
In Ratatouille, the title dish proves to be a Comfort Food for Anton Ego, as evidenced by the tears of joy and happy memories of his mother when he ate Remy's slightly fancied-up version. The experience was enough to cause a complete change of heart.
Literature
In one of the books in The Pendragon Adventure, Bobby appears in modern-day Stony Brook where his Muggle friends live, and they go to their local fast-food hangout for fries.
In Harry Potter, the standard treatment to recover from a Dementor attack is chocolate. (Some Truth in Television here; chocolate is known to have mood-elevating effects).
Live Action TV
In Doctor Who after the Doctor explains to Rose that he's the last of the Time Lords, and what that actually means, they go out for chips. The chips help.
In Supernatural, when Castiel abandons his host body, we get to see said host body, Jimmy, chow down on cheeseburgers to the point of grossing Dean out.
In Parks and Recreation, cheesburgers are one of two known cures for Andy's 'shoe shine head' ailment.
In The Drew Carey Show episode "The High Road to China", Drew is stranded in China with no money and without his passport. He gets some money by working locally and upon arriving in Beijing, almost immediately goes to the McDonald's there. Unfortunately, he still hasn't got enough even for a Big Mac, prompting him to say "I never thought I'd use this in real life, but 'I will gladly pay you Tuesday for a hamburger today.'".
It is mentioned in an episode of Babylon 5 that Michael Garibaldi eats like a starved man after experiencing serious personal tragedy, though only one early episode draws any particular attention to it. Worth noting that he is consistently depicted as being an excellent cook, particularly when it comes to Italian cuisine. He is also an alcoholic, so the food could also be a sort of Addiction Displacement.
Tater tots for Mercedes in Glee. Naturally, she is not happy when they are banned.
In Fraggle Rock, radish bars are Comfort Food to Red and Mokey Fraggle. They even sing a song about it!
Buffy's visit to Los Angeles after she's Back from the Dead must have been really intense, she brings back a Buffy sized tub of chicken.
The Nostalgia Chick stuffs herself with Subway and Dairy Queen when she's feeling depressed.
Team Kimba of the Whateley Universe and Chou's Moon Pies. The rest of the team has their own comfort foods (Lancer's is pork rinds), but Phase is appalled by all of them since he has the refined palate of a food critic.
In Homestar Runner, after his Lappy got swiped, Strong Bad gorged himself on various chips, which he claimed to be his anti-depressant.
Troper Works
In Space Beasts Ichabod Crane (not that one) really likes a good cup of chamomile tea after a humiliating experience
Also his girlfriend Marzipan the Cat Girl wanted a hamburger with extra onions after being held captive for three weeks by aliens.
