Table Manners: What is metagaming?

One of the most unique aspects of roleplaying games is that players aren't just players — they're also characters and audiences. But that means that sometimes, for the sake of the story, that they need to be careful not to let their desires as audience members influence their actions as characters.
Metagaming is when a player acts on information their character doesn't have, usually spoiling the fun for the other players. The idea is that since the character is a different person who grew up in a different world and has had unique experiences, there are a lot of things that the character knows that the player doesn’t, and vise versa.
I don’t know how to cook a delicious pie, but my 160-year-old half-elven grandma sorcerer Nina does. Likewise, Nina does not own a Monster Manual, and therefore she doesn’t know the challenge rating and vulnerabilities of every evil creature she may meet.

OOC talk

Some new players get metagaming mixed up with out-of-character talk. While the etymology of the word may suggest those are the same (“meta” meaning “outside,” so metagaming means stuff outside the game), the terms usually have different meanings in the community. OOC talk is just stuff a player says that the character doesn’t say. Some OOC talk is necessary to play the game -- players need to ask the DM about rules and rolls, after all. OOC talk is only bad when it slows down the game, detracts from opportunities to roleplay or leads to metagaming.

One reason metagaming is frowned upon is because it doesn't respect the fiction. Shouting “Don't go in there, you sexy moron!” at the TV while watching a horror movie is so common it's cliche now, but it's a familiar situation that helps illustrate metagaming.

Oh, the horror

If I, Steve, play sexy moron Chaz Buttchin in a horror movie, I know that I'm in a horror movie. Chaz doesn't. I know that there's been a breakout at the asylum upstate because I've read the script. Chaz hasn't. I know in what moments the soundtrack is going to add ominous strings, but Chaz doesn't. Chaz is having a normal day (Or maybe he's having a slightly more-inconvenient-than-normal day where his car breaks down and he's meeting an awful lot of old people who laugh in an unsettling way, but still. Normal day.).
Now, you could write a horror movie with a smart protagonist, but even then, there will be points at which even a smart hero will do things that an audience member will think are dumb. That's because the filmmaker is employing dramatic irony: situations in which the audience knows something a character doesn't. The filmmaker put the scene where the immortal serial-killing avatar of chaos escapes from his restraints to start developing tension.
In horror fiction, the line between sexy morons and smart heroes who just don't have all the facts can get pretty blurry. Storytellers will ask you to suspend disbelief -- they ask you, for the sake of the story, to accept something as implausible as a person investigating a creepy, dark house even though their flashlight batteries just died -- on the promise that suspending disbelief will allow the storyteller to pay the audience back in the form of thrills, chills and jump scares.

Smart? Maybe. Fun? No.

Back in the world of D&D, metagaming is when a player (who is both character and audience) chooses to discard dramatic irony. They're not only yelling at the TV as audience members, they're doing the impossible as characters and hearing what the audience is yelling.
Most beginners who metagame aren't doing it on purpose, but there are a few players who do it even when they know better. They might do it to seem smart, they might do it to gain an unfair advantage over other players, but they're really just ruining the fun. They might argue that they're only trying to be realistic, but metagaming usually makes the story much harder to believe.
There's a good example of how it can backfire when a character disregards the conventions of storytelling for the sake of logic in Community.