If you look at the picture of the MKS Sylvan road pedal I posted above, on the right end of the pedal, you will see a protrusion pointing up. That is what I always thought was the quill for which the pedal is named. Tom up above says quill pedals are typically so narrow that the his shoe doesn't stay inside the quill and the quills pain his feet. My wag is that Tom thinks about quills as I do. But looking over the internet, it appears that the term includes all sorts of pedals, including the likes of MKS touring pedals, that don't have what Tom and I thought was the quill. So, it seems that any parallel plate rat trap type pedal is a quill pedal inclucing traditional road pedals like Campagnolo, etc. What the quill on those pedals is, I don't know, unless it refers to the serrated edges.

A quill stem is a stem with a prong that enters a tube and has some sort of jam wedge or cone to secure the stem to the inside of the steerer. Threaded headsets take quill stems. I guess the metaphor is to a porcupine quill with a securing barb.