This is a term referring to video game characters other than the one guided by the person playing.
The term originated with paper-and-dice role playing games, specifically the Dungeons & Dragons ancestor Chainmail. It refers to characters that are operated by the game engine or game master. These characters are generally less "rounded" — they don't have much Character Development, unless the dev team or gamemaster is exceptionally skilled. Players will sometimes determine that an NPC has plot significance based on the fact that the GM is presenting the character with more details than usual.
But at least in that format, the non-player characters have the ability to engage in conversation and go about a daily routine. When it comes to the vast majority of computer games, an NPC's entire existence will consist of walking back and forth (typically right where you don't want them to be in 2D games) and saying the same line of dialogue over and over again. (That is if they have the honor of being able to move; sometimes they just stare in one direction until you talk to them.) Though, if necessary, they can move with such speed and access that the player can only dream about. A privileged few may be made into Quest Givers, temporarily giving them some small worth in the eyes of passing protagonists. A sufficiently cool NPC may even be Promoted to Playable.
The term is sometimes, in tabletop-derived computer games, used to refer to any non-hostile character that the player did not create directly, even if the player has near-complete control of them for gameplay purposes. In fact, it has even been used to specifically refer to those characters that can join the player's group and be controlled by them but are not the one specific character representing the player.
Oddly, NPCs, despite being normally clueless, can find out about things that happened miles away and even know about all of your skills and past deeds like they're all connected...
This in recent times has been used as a snarl word in political discourse, often used to label an opposing view as being though it came from people "programmed" by the media (and political correctness by extension), or by influential speakers. Please do not pothole to this term as a Take That! against your opponents. If you want to highlight a character who is a blind zealot, the trope you're looking for is Strawman Political.
The counterpart, of course, is the Player Character.