Non-Player Character. In general, any character (human or otherwise) in a role-playing
game that is not controlled by someone playing the
game.
In a tabletop RPG, the game master or equivalent (the person running the
game)
will generally act/speak the parts of all NPCs. These NPCs can range anywhere from an innkeeper the players talk to in order to rent a room to the mysterious woman who follows your
party along for her own unknown reasons only to backstab you right when you were starting to trust her. It's up to the GM.
In LARP, the people running the game
will again play the NPC parts, and
may enlist others to be NPCs. In an ongoing game, LARP NPCs tend to be the characters who are either too temporary or too important to be done by a given player.
In single-player video game RPGs, NPCs are anyone who isn't your
party. They generally aren't referred to as such in this context because "the guy next to the weapon shop" works just as well. These NPCs have a set dialog, and most
will repeat the same thing they say every
time you try to talk to them. Several webcomics have poked fun at this.
And in a MMORPG, the NPCs are the characters controlled by the server. They often have some kind of distinguishing feature, such as listing their trade in their status window or their
name being displayed in a different color of text. As with single-player RPGs, these NPCs
will tend to have set patterns of behavior and often must be interacted with to achieve some objective or another.