xDownloader v1.0 is a Cydia-like homebrew application specially made for the PSP, and created by French developer J3r3mie. Looks like he's already beat all the other drafters of Cydia on the PSP.

The functions, as it is similar to Cydia, works pretty much the same as its iPhone counterpart. You can use it to download apps, games, themes, anything else you might want on your PSP. And this is all done direct to your PSP's memstick.

Instructions (translated by Google, from the Readme):

* Download the archive xDownloader v1.0 .and uncompress it to the root of your Memory Stick.
* XDownloader since the launch of the PSP XMB and you're away.

By the way, the app's in French.