Many game companies released downloadable demo versions of their games for the PSP. Most of these can run in PPSSPP. These files are legal and free to download.
Unfortunately the PSP Demo Center that used to host them is no longer online.
There's a new site though that has quite a few: PlayDreamCreate.
The PSP was released in 2005, and contained a number of bugs that made it easy to run your own code on the device. A large community of hackers emerged who figured out how it worked and wrote their own software for the device. There's now a lot of little homemade games to run, and a free homebrew "SDK" (software development kit) to make your own.
If you have manually downloaded homebrew, unzip it and put the game folder in PSP/GAME in your memstick directory.