welcome to pspmod
Firmware is the operating system of the psp. When the psp first came out it had no security against applications that was not made by sony, so people created emulators and apps and used them as they pleased. However sony saw that running emulators and apps could make them lose money, so they updated the firmware and put in security against those homebrew apps so the psp could only run programs with their signature on it. So then their was the discovery of methods to carry your psp back down to the 1.5 firmware which had no security against homebrew so you could play emulators.
But sony in their infinite wisdom decided to release games with the latest update on it and they put in security in the game that made the game unable to run on lower firmware than what came packaged with it, so if you stayed on 1.5 you would lose the ability to play the latest games.
Then a man named dark alex came up with the brilliant idea to modify sony's latest firmware so that it removes the security checks and is able to run homebrew and iso( backups of your psp games on your memory card), and then cfw(custom firmware was formed.
you may also find this helpful
http://www.pspmod.com/forums/psp-har...ictionary.html (PSP Modifcation Dictionary)