The ZIP code thing has been fairly well covered. It is a "location specific" code that can be used for mail routing. The basic 5-digit codes gets the mail (usually) to a specific "letter carrier's" route. Or at least to a specific Postal substation.

The "extended zip code," the added digits, should be specific to a particular "mailbox."

The actual use of the ZIP code is premised on someone actually reading what is written, and entering the ZIP code so that it is printed in barcode along the bottom of the envelope. After that, the letter can be processed "by machine." Only large or "central" POs (technically "mail distribution centers") actually bother to "barcode" stuff, and mail that you recieve without a bar code probably hasn't benefited from having the ZIP in the address.

Mail with the extended ZIP - all 9 digits - should be deliverable with no other address, but it ain't gonna happen. In practice, the actual delivery person doesn't use the ZIPS, and will send it back to the "dead letter office" - which is equivalent to discarding it, in many cases.

Some addresses may have both a PO Box and a "street address." According to mail instructions in company phone books (Raytheon and Boeing, among others) the USPS practice is to use whichever is listed first.

The distribution centers will "hand sort" anything without a ZIP, and the delay is not that serious (if everybody's in a good mood there on that day).

If the delivery person can't make out the right street address (or PO Box number), turnaround for someone to look at it and "hand address" a correction may run up to 3 months. (Or "unto forever.")

All of above based mostly on personal experience.

John