Doggy Style is one of many sexual positions. The woman (or a passive gay male) gets on hands and knees, while the male (or a female wearing a strap-on) positions themselves behind the person on their hands and knees, and penetrates them.
This position gets it name from the fact that it is quite similar to the position that canines use to copulate. Many people seem to think that it allows for deeper penetration. It also stimulates areas of the woman's vagina that are not normally stimulated by the missionary position.
Variations of this position are also used. A woman can bend over the arm of a couch or chair, for example, a desk, a counter, or any number of everyday objects.