Clipless shoes are the ones with cleats and clips on the pedal that the cleat clips into. So why in the world are the called clipless?
It has to do with the difference between pedals with toe clips and clipless pedals.
Pedals with Toe Clips
Clipless Pedals (and shoes)
The clipless shoes are for the clipless pedals.
The wikipedia page says the following:
The confusion comes from the word "clip" being both a noun and a verb.
Clip as a noun:
This describes the old-school pedals with the leather (or vinyl) straps that strap the foot down to the pedal.
"Clip-less" pedals do not have the aforementioned securing strap. They (obviously) use a different system.
Using "Clip" as a verb to refer to securing something (and not cutting something) is called "conversion" (linguistic term) or "verbing" (non offial term).
So, saying "Clip into your pedals." is similar to saying "I'm tabling this discussion." It's taking a noun and converting it into a verb.
So, we cyclists confused ourselves :D