Most likely you have 1 of 2 pieces used to make a novelty item called a Magician's Coin. These sell regularly on eBay for a couple dollars, but if you just have the one piece I don't think it's worth anything. With so many people asking about coins like this, and no articles in major coin publications (to my knowledge) nor discussions between dealers about them, this has to be some kind of after-mint alteration. To be sure, you can get a free first-hand professional appraisal by ANACS by bringing your coin to any coin show they attend. Their list of shows is here : http://www.anacs.com/shows.html
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The head of a penny is obviously the queens head, and the tail is that thing on the other side of the penny.
A penny!
The side that has the Presidents face on it is the head making the other side the tail.
One side of a coin usually has a "head" of someone. The other side is the tail.
This sounds like a "misaligned die" error. That happens when the 2 halves of the coin press don't meet squarely on the coin blank. One side will be struck correctly and the other will be off center. Unfortunately it's not a very rare error so it would probably retail for a few dollars at most.