Pizza crust in general is the baked
dough part of a
pizza, which includes the part under the
toppings, but when most people talk about pizza crust (as in eating the crust, or
stuffed-crust pizza) they mean the edge parts specifically.
It used to be a lot of pizza crust went to waste. Ironically, many people would order breadsticks at extra cost and yet throw away the pizza crusts that came with the pizza for free. Then around the mid-90s pizza places (in Virginia at least; possibly earlier elsewhere, I wouldn't know) started including various kinds of dipping sauce; Papa John's is most known for this now but others do it as well.
With the advent of dipping sauce, pizza crust started to become a delicacy in its own right; in fact Papa John's breadsticks are nothing more than pizza dough baked in strips, till they're almost like self-contained crusts.