How is a recumbent bike different from a normal bike?

A normal bike has you riding upright or hunched forward while a recumbent has you leaning backwards, like in a reclining chair.

IMPROVING ANSWER: A recumbent bike is not as good for going up steep hills, because you cannot stand on the pedals and use your body weight. Your legs go in front of you, not underneath you. Also, I find that I like to lift my buttocks off the seat every few minutes for comfort and good circulation, but this is difficult or impossible while riding a recumbent. Also, a recumbent is difficult to steer for new riders, but only for the first hour of riding of the first day. A regular bicycle doesn't really use the turning of the handlebars to turn--it uses the shifting of your body weight. At low speeds a recumbent will actually turn by conventional steering, and this is a difference that takes some getting used to. One last thing: The handlebars on some recumbents have to be high, putting your hands up near your shoulder level, so that if you turn the handlebars while pedaling your knees will not strike the handlebars. I like my recumbent bike and my diamond-frame standard bike also.