Basically, the above posts are right. If there is sorting equipment at the destination Post Office, it helps them with automated sorting. And - since individuals very seldom have access to, and are not required to use all 9, I would hazard a guess that mass-mailers with computerized lists ARE either required to use, or receive a deeper postage discount for using the full zip+4.
The first five digits are the Post Office itself, or in some cases, a large corporation or university may have a dedicated zip.
If you ever see a P.O. Box address with 9 digits, the last 4 are either the P.O. Box, or obviously related to it.
So...if I'm an individual mailing Christmas cards, it wouldn't make any sense for me to use a 9-digit zip code?
The 9-digit zip code only makes sense if you're a business doing mass mailings?