In simpler terms, it gives someone more control over a computer than the person sitting at the console, and the person at that box has next to no way of detecting Back Orifice once it's been installed on the computer.
Back Orifice gives control of such things including, but not limited to: the file system, the computer's processes and registry, and any multimedia devices attached (webcams, etc.). A hacker would also be able to retrieve almost any information cached by the OS, including any passwords that are used by the computer's owner/operator.
The only real cure for a computer infected with Back Orifice would be to reformat your hard drive, since BO can be configured to attach itself to just about everything.
-Awww, shit! I picked up Back Orifice somewhere and now I've lost all my files to some god-damn hacker.