How an exploit works is fairly easy. A glitch in a game or system function (i.e. TIFF Exploits, MOHH exploit, wipeout pure exploit, etc.) to allow unsigned code to be run. This means that the PSP can now run code that Sony or the game maker has not written themselves. That means you can use the exploit to run a program which installs a CFW. Once that CFW is on, then a check for signed code is eliminated and any Homebrew can be run.