A third wheel is someone in a group who's sort of just hanging around. Have you hung around two people who are getting along really, really well, and you're sort of being ignored because of that? You are the third wheel.
I've always found the ''third wheel'' thing to be a silly analogy. Vehicles with two wheels are immensely unstable when you take the all momentum away. A third wheel (assuming it's not mounted stupidly on the outer most corner from the centre of gravity or something) applies a great deal of stability.
Now, being the third leg, second head, 25.1th wheel, first snooki and third shoe, are all immensely useless things. They'd fit the analogy better.