MAME stands for Multiple Arcade Machine Emulator.
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. The source code to MAME serves as this documentation. The fact that the games are playable serves primarily to validate the accuracy of the documentation (how else can you prove that you have recreated the hardware faithfully)?