MAME or M.A.M.E. [Multiple Arcade Machine Emulator] is a hardware emulator that supports over 2000 unique arcade machines

The MAME software actually emulates the hardware used in arcade machines, like the pang PCB on the left.

When MAME is run using ROMS (the original arcade game program), that were 'dumped' from the original game board, MAME faithfully* reproduces the arcade game on your PC/MAC...or whatever.

*in some cases MAME is unable to faithfully reproduce the original arcade machine due to hardware limitations or incomplete emulation. With many non-working games, games where the software hasn't been dumped and encrypted hardware/software which makes some games unplayable or not available at all.

The purpose of the MAME project is to document the hardware (and software) of the arcade games. The side effect to this is that you can actually run arcade software on your PC, MAC, Xbox or converted cabinet.

There are already many dead arcade boards, whose function has been brought to life in MAME. Being able to play the games is just a nice side-effect. The huge success of MAME would not be possible without the talent of the programmers who joined to form the MAME team. At the moment, there are about 100 people on the team, but there is a large number of contributors outside the team too. Nicola Salmoria is still the coordinator of the project. 

MAME is a stand-alone application that does NOT contain any games and requires the appropriate ROMs [games] to run your favorite arcade game.

There is no completion date for MAME. This is due to many factors including the time it takes for the developers to write the software, who incidentally work for FREE, and the huge number of arcade machines produced since the 70's, and the varying types of 'encrypted hardware' that was used to stop arcade operators copying the games.