Generally speaking, the act of killing someone in a first person shooter game with a one shot gun (sniper rifle, bolt action rifle, etc) without using a telescopic sight or sniper scope. Most commonly, the term is used to mean that you fired such a gun from the hip and killed someone with it, however it can also (debatably) mean that you pulled up iron sights on a sniper rifle / bolt action rifle and then killed someone that way. The term does not apply to shotguns, semi-automatic rifles (unless they can be scoped), or any automatic weapon.
No scoping is generally viewed as an act of skill (or luck, depending on who you talk to and the mechanics of the game you're playing). This is because you are killing someone with one shot through a (usually) large crosshair and also risk exposing yourself if you miss. However, the amount of prestige that is attached to a single no scope depends on the distance and rate of success; i.e. if you no scope once and do this by killing a guy who you are literally next to, that doesn't take much skill, but if you continually no scope guys who are halfway across the map, that's some seriously good shit on your behalf. On a related note, no scope headshots get you some serious prestige if you can pull them off constantly.
Example (in COD5):
Player 1: Damn, I just no scoped some guy on