A platfomer is a game genre wherein players control a character by jumping or otherwise operating on physical (virtual) platforms. Mario and his impressive jumping abilities are pretty much the defining trend of the genre. (Games of this sort for the Vectrex include Spike and Spike Hoppin'.) Gameplay tends to be simplistic, usually involving only one or two dynamics for using the character to solve puzzles or defeat enemies.
2D platformers, or two-dimensional platformers, are typically side-scrolling games (such as the Super Spike World demo on the Space Frenzy cartridge), either freeform or with a constantly moving screen to force player movement and simplify scripted events.