This one drives me so crazy that I am devoting an entire page to it. I have read so many posts and heard so many conversations where this question was not directly answered or it wasn't clear that the newbie biker was utterly confused by this terminology.
Yes, you "clip in" to clipless pedals. There are several different styles (Look, SPD, SpeedPlay, etc.), but, if you have special bike shoe with a cleat on the bottom that clips into your pedal that is known as a "clipless" pedal system. It baffles me that this terminology has become industry standard.
The term "clipless" refers to the lack of a toe cage which can be used with standard street shoes to allow the foot to pull up on the pedal. This toe cage is also known as a "clip", so, bike shoes that fasten directly to the pedal do not need this "clip" and are therefore "clipless"