The autorun would be put into the root of the USB Flash Drive. Once the USB drive is plugged into the computer, the autorun is initiated and will do whatever it is programmed to do. Display extra options in the AutoPlay menu, run a hidden program, copy files, pretty much anything.
It is one way viruses and worms travel from computer to computer.
Don't be worried though. If you have an updated antivirus software, chances are you will be safe.
In all my travels, I have only encountered a similar virus once (The Kavo virus). It originated from my friend's laptop and worked its way to two of my USB Flash Drives, two desktop computers and one laptop, just by using one simple autorun.