It's just like the name says: it allows you to play PSP* games on your android device. It does not provide the game files (called ROMs) but a quick search on the internet will provide you with all the files you'll need.
It does not run EVERY game, though. And some games might make you think you are watching a slideshow. Apart from that, the ones that work give you the full PSP experience.
Some devices like Samsung Galaxy S7 might not be fully supported.
List of games that work on most devices:
Persona 2, Persona 3 Portable, Dragon Ball Z, Little Big Planet, Burnout Legends, Burnout Dominator, Final Fantasy : Crisis Core, Final Fantasy : Type-0, Monster Hunter 2 Unite and 3: HD Remake, Soul Calibur, Tekken: Dark Resurrection and Tekken 6, Grand Theft Auto LCS / VCS, Lumines, Worms, Wipeout.
Head over to http://www.ppsspp.org for more information.
* PSP is a trademark of Sony, Inc. Please download roms for games that you really own.