Essentially, a ROM is a program of a retro game, and ROMS can be played on your PSP if you first donload the proper emulator (ie a SNES emu for a SNES ROM) onto your PSP, then place the ROMs in the emulator. Everything has got to be in certain folders though.
As far as the legality of downloading ROMs, I could give a crap. Here's my excuse :) If a friend owns an old copy of Super Mario World on the SNES, it's basically like I'm giving him my PSP as a gift, he's putting it on there, and then decides to give it back to me. just skipping all those inconvenient steps:D
Seriously though, no one cares about illegally downloaded ROMS.