Here is a good explanation of MAME + ROMS

NOTE: Please read legal implications on MAME™ ROM usage from Northwestern University Law School before downloading any ROMs to ensure legal compliance.

ROM files are the arcade games that were sucked out of the real arcade machines. The MAME™ software pretends to be the real arcade machine to run these ROM games on your PC. No ROM files are included with the MAME™ software, nor do we host any of these files. You can find more information on MAME™ ROM files by searching Google™. 

If you own the original games, there are also services to get them on DVD here and here.

IMPORTANT: The versions of ROMs you use should match the version of MAME you are using, or they will not work. You can use ClrMAMEpro to audit and fix your ROMs, a guide for using it can be found here, or here with a video turorial at the bottom.