NPC
An Non Player Character is a character under the control of the GM. They are there to provide backstory and life to a campaign, and to advance plot hooks. The role of the NPC is essentially to provide external life to the game so the players have an avenue to suspend their disbelief that they are just sweaty guys in a basement with a bunch of dice. A world full of NPCs who are played well can lend credence to the reality of the world.
Sadly, this doesn't always happen, and the NPC is abused by many a DM who either doesn't know any better, or is a raging prick.
Types of NPCs
Inhabitant
These NPCs act as normal people would. Going about daily lives, maybe interacting with the characters, maybe not. They aren't spectacular in any way, but they're realistic. This is a Good NPC.
Lackey
A dumb NPC that's there simply to take direction from the PCs. No free will to speak of, and is often used as a meat shield when danger arises. This is a Crap NPC.
Hirling
Similar to a Lackey, but a bit smarter. They get surly and won't interpose themselves between the PCs and danger willingly. This is a Good NPC.
Vend-O-Mat
Usually a cleric, these NPCs act as mobile vending machines, dispensing healing spells or buffs at the push of a button. They usually have no personality. This is a Bad NPC.
Psychopath
Fucked up for no reason. Brilliant in conversation, stupid in action. Exist solely to add 'flavor' to a DM campaign. Once in a blue moon, this NPC is tolerable. As a regular, he shifts from Crap NPC to Bad NPC.
DMPC
The DM really wanted to play, and so made a character up. Only now, he's in control so things tend to go the NPCs way. He will often be min-maxed, but arbitrarily so, as the abilities seem to change with the encounters as they require. This is a Bad NPC.
Gary-Stu/Mary-Sue DMPC
As above, but with features that resemble the DM or his girlfriend. This is what the DM wants to be in his fantasy. There usually is a wallotext dialog from the NPC explaining his backstory, even if you just asked him for directions to a brothel. This is a Horrendously Bad NPC.