"Platformers" refer a certain type of action game
where the majority of the game is spent (appropriately enough) jumping from platform to platform (i.e. bottomless pits
are one of the main enemies).
Although it's not the first platformer (Pitfall gets that distinction), Super Mario Brothers is generally recognized as one of the paragons of the genre. Some of the most famous of the 2-d platformers include Mega Man, Castlevania, and Sonic the Hedgehog.
This was one of the most popular video game genres until 3-d games became the norm with the advent of the Sony Playstation.
Although the genre is less popular now, there are several 3-d platformers, the most notable being the Crash Bandicoot series, Mario 64, the Sonic Adventure series, and Rayman 2. Developers are having growing pains moving the genre into 3-d, as most gamers end up cursing the camera, as it seems to tilt in "just the wrong direction" whenever that vital jump has to be made.