Bricking is when your PSP no longer works due to a damaged flash. This can happen if you turn your psp off while updating your firmware. Unbricking is when you use a pandora battery and magic memory stick to repair your psp. Homebrew firmware aka custom firmware is....customized firmware for the psp that allows you to play games from your memory stick and load homebrew applications.
You can buy a pandora battery and memory stick by clicking my signature.