According to the United States Postal Service:

ZIP is an acronym for Zone Improvement Plan. A ZIP Code is a 5-digit code that identifies a specific geographic delivery area. ZIP Codes can represent an area within a state (an area that may or may not cross county boundaries), an area that crosses state boundaries (an unusual condition), or a single building or company that has a very high mail volume.

The "extra" four digits that appear after the main body of numbers in the zip code do often denote post office box numbers. They can also link a street address to a specific area within that identified by the first five numbers.