I made a few stabs at trying to describe this succinctly with a few examples, but I couldn't do it. If you start using OOP (perhaps browse PHPClasses.org or try out PHP's new DOM XML functions) on a regular basis, you'll understand the advantages. Barring that, I can only provide you with links to other discussions on the subject. If you search Google for "OOP advantages" or something similar, you'll find plenty. This thread
on the evolt mailing is quite an extensive discussion stemming from a question similar to yours. Click on the [thread] link to see the whole thread, which might make it a little easier to navigate.
Sorry I can't provide you with a better answer. When I first was learning OOP (in a Java course), I didn't get it at first, but then one day it just "clicked" and I understood all of the possibilities it provides. Maybe someone else here can better describe its advantages.