As I understand it, the first 3 digits of the zip code indicate a distribution center. Some distribution centers have several 3 digit codes assigned. The last 2 digits are assigned in alphabetical order to communities served by the distribution center.

So, I live in Ann Arbor, which is served by a distribution center in Detroit. My zip code (at work) is 48104. Down the road a few miles is the city of Ypsilanti, which includes a zip code 48197. The city of Detroit has zip codes starting 482. So we can see that the Detroit distribution center belongs to at least 481 and 482.

Apparently, a distribution center in one state does not serve communities in a neighboring state, so we get white lines between states with (almost) no scribbles crossing them.

Wikipedia's zip code article says "the first three digits of the ZIP code, ... describe the region of the country". See it for lots more info.