I took a grad-level quantum computing class which I didn't quite have the physics background for, and the lecture that lost me, about 3 weeks in, was on the different kinds of physical gates quantum computers use.

My recollection is that there were 3 necessary gates for a quantum functionally complete set: One gate was classically functionally complete, the other two are where I got lost. Can you explain like I'm 5 (or explain like I'm an undergrad with minimal QM knowledge) what these other gates are doing?

Thanks!