MAME emulates classic arcade games: everything from Pac-Man to Burger Time. Of course, many of the ROMs you need to be able to play games like that are copyrighted — so if you want to play Galaga then it's dubiously legal. But if you worry about things like that, there are free games which you can play without breaking any law.
Anyway, as for the Chrome port, you have Google engineer Robert Muth to thank for carefully working out how to get it running. He also posted a detailed case study of the challenges he faced along the way in the four-day project.
But you probably want to play some games, right? So you should head over to the Chrome Web Store and install the classic Robby Roto arcade game. That's one of the copyright-free games we're all entitled to play. Once you've gotten that, though, you can upload any MAME ROMs you happen to, uh, "find" and play them through Chrome. Sweet. [Chrome App Store via Slashdot]