MAME stands for Multiple Arcade Machine Emulator. When used in conjunction with an arcade game's data files (ROMs), MAME will more or less faithfully reproduce that game on a PC. MAME can currently emulate over 3000 unique (and over 5400 in total) classic arcade video games from the three decades of video games - '70s, '80s and '90s, and even some from the current millennium.
The ROM images that MAME utilizes are "dumped" from arcade games' original circuit-board ROM chips. MAME becomes the "hardware" for the games, taking the place of their original CPUs and support chips. Therefore, these games are NOT simulations, but the actual, original games that appeared in arcades.
MAME's purpose is to preserve these decades of video-game history. As gaming technology continues to rush forward, MAME prevents these important "vintage" games from being lost and forgotten. This is achieved by documenting the hardware and how it functions, thanks to the talent of programmers from the MAME team and from other contributors. Being able to play the games is just a nice side-effect, which doesn't happen all the time. MAME strives for emulating the games faithfully.