IMAP v/S POP
Let's say you have two computers, one at home and the other at work. Each is running Eudora™ and each is set to use POP. You have both set to download mail but leave a copy of the your mail on the POP server.
You go to work and start up your Work Computer and run the Eudora™ Application. Eudora™ grabs all the messages in your inbox and downloads them to your computer (while leaving a copy of each message on the server). You read a message ME in your inbox and reply to it. The reply goes into your "Sent Messages" mailbox. But, like all other messages in your "Sent Messages" mailbox, your reply to ME is saved on your work machine's hard drive.
Later, you go home and run your Eudora™ on the home machine. And Eudora™ then downloads all the messages in your inbox to your Home computer's hard drive (while keeping a copy of each message on the POP server). You see the message that I sent you in the morning (the one to which you replied earlier at work) and a new message from Me. This time, I say that he lost your original reply and could you please resend him the reply. Ooops! You have a copy of the reply, but it is on the hard drive of the work machine and not on the home machine at all (unless you send yourself a copy of all messages you send ... but this can become cumbersome).
With IMAP, -all- your mailboxes are typically kept on the server (not just a copy of what's been downloaded into a local inbox). The has another advantage ... it means you can use -any- IMAP client (not just Eudora™'s) to view messages. This is especially nice when you have to use somebody else's computer to view your e-mail. It also means you can use web clients (like UIC's WebMail) when there is no Eudora™ around... say, just a machine with a web browser. Most IMAP clients these days cache your mail locally (this means you can work with most applications offline, just like you can with Eudora's POP client).
Not that POP is bad and IMAP is good ... it depends on how you typically deal with e-mail. If you are very mobile and use a lot of client machines, then IMAP is a good thing. If you're only using a couple of machines, and you're willing to live with the fact that only your inbox will be duplicated on each client, then POP is fine.