Think about it like this: ASU (Arizona State University) has 3 campuses; one in Tempe (main campus), one in Queen Creek, and one in Phoenix. Since the Tempe campus is the main campus they set up a wi-fi network from one ip address. An NAT allows that one IP address to be assigned to the other two campuses, both located about 30 miles from eachother. That way all three campuses have wi-fi, but they are all connected to that one IP address from three different locations.