The difference is where the messages are stored. with POP3 you copy the message to your local PC and delete it from the server, either immeadiatly, or after a few days depending on how you have things configured. This means it's not there for your other PC/handheld.

With IMAP the messages stay on the server, and are fetched on an as-needed basis, and you can have folders on the server. You can have local copies by synchronising your folders to your pc, and then work off-line and re-synchronise when you next connect. This is often the best way to work.

An advantage of IMAP is that you can use websieve to pre-file messages as they are delivered into different folders.

The big benefit of IMAP is that you can use any browser and webmail to pick up your email when you are out of the office, your mail is not on the pc locked in your office.