What they are supposed to do is what their name suggests extend the penis's girth or length or length and girth! A good penis extender will fit snugly around the erect penis and be thin enough to transmit sensation that feel similar to a condom does. They do not replace condoms though as some are porous and can transmit viruses. I have heard anecdotal evidence of people getting pregnant using extenders as well.
They are supposed to give women a new sensation of being full and can help men who are learning to extend their orgasm or dealing with premature ejaculation (because most extenders reduce sensation).
Personally I find that they are about as much fun as a dildo and can lend a bit of difference if we are roleplaying something like a gang bang but they won't make for 'shooting fireworks' type sex. If you catch my meaning! They can be fun though, as long as your guy (or you!) don't have some issues with feeling inadequate. In my opinion (and my guys) nothing beats skin on skin, but an extender can be a little something different.