Shocking enough, you "clip in" to clipless pedals; your shoes attach to the pedals. You need bike shoes to use them.

From Sheldon Brown:
"Clipless Pedals

Up until the late '80s, the choice was between plain pedals or pedals with toe clips and straps. Since "clipless" pedals provided a way to have a secure attachment to the pedal without the use of toe clips, the name stuck, even though it is sometimes confusing to newcomers. "Clipless" or "Step-in" pedals use a mechanism similar to a ski binding. In fact the first successful system was made by a ski binding manufacturer, Look. Clipless pedals use a cleat which is bolted to the bottom of the shoe. When the rider steps on the pedal with the cleat, the cleat locks into the pedals mechanism, and is held firmly in place. Some systems hold the foot at a fixed angle, others allow various amounts of "float", or angular rotation of the foot on the pedal.
With most clipless pedal systems, the foot is disengaged by twisting the heel outward. Some of the earlier systems, such as the pioneering Cinelli model, required the rider to reach down and operate a release mechanism by hand. This style is sometimes jocularly referred to as "death cleats.""