If you primarily use one computer to read and write your email from, POP3 works really nice. All your email is stored on your local computer, you can access it and store it as you like. But POP3 works really bad when you use multple sets of computers to read and write email. While I access my email from just about everywhere, there are two primary places I read it: at work and at home. If I were to use POP3 to read my mail, it would "download" all my email to whatever computer I was on at the time. So if I read my email at work and downloaded it all to my computer at work, I would not be able to access that email from home uness I uploaded it back to the server. And if I save a bunch of email at home and want to get at it from work, I can't get at it unless I resend it to myself.
For the very reason of staying in sync, I basically avoid using POP mail clients. To insure I knew where all my email was, I used a Unix shell account and, as necessary, used POP mail clients to download and decode email attachments. But now, thanks to IMAP, I don't have to do that anymore. IMAP stands for "Internet Mail Access Protocol" and is an up and coming standard for mail access. It's not quite as ubiqutous as POP3 is yet, but the current IMAP4 standard is being implemented in many new email products like Netscape Communicator and Microsoft Outlook.
IMAP4 and POP3 are both standards hashed out by the Internet Engineering Task Force, both have their own RFC's (or Request for Comments, which are basically well documented and open Internet-based standards), and they accomplish similar things and work much the same way. IMAP and POP both require a "server" set up that has access to your email. A piece of client software is then configured to access this server. The client and server then "talk," exchanging email as appropriate. These servers are very different, however. You must have a client that supports the protocol and it must be configured correctly. Your ISP should be able to tell you if they support these standards and how you would need to configure your client software to take advantage of it.
IMAP works really well when you use multiple computers to read your email, but even if you only read your email from a single computer, there are two convincing reasons to use IMAP over POP: It will save you time and it's somewhat more secure.
Because POP3 was designed primarily as an "offline" mail reading solution, POP3 clients usually require you to "download" all your email before you read it. IMAP can function this way, but it also works in an "online" and a "disconnected" state. In a disconnected state, you can work with "local" copies of stuff you have downloaded previously. In an online state (usually the default), you access your email directly on the server. You get a listing of messages in each "folder" and download messages only as they are read. You can store your email on the server in "folders" for later retrieval and can easily get at them again. This bandwidth-friendly approach means you only download what you need to and nothing more.
IMAP has an important security feature built into it, which alone makes IMAP worth considering. With POP, your "password" is transmitted in the clear, which means anyone listening on the network can make a note of your password, pretend to be you, and read your mail without you knowing. IMAP implements a sort of "challenge-response" system based on your private password. Your real password is never typed in the clear and the challenge-response is done in such a way that, given the challenge and the response, there is no way to determine what your actual password is. An extension to POP, called Authenticated POP (or APOP), does something similar, but is supported by even fewer email clients than IMAP4 currently is.
Given that not a lot of ISPs are implementing IMAP as of yet, you may not have much choice in the matter as to which standard you can use today. IMAP is still gaining acceptance throughout the Internet community, but when you have the opportunity to use it, you should. The added functionality is quite cool. More information on IMAP can be found on the IMAP server (http://www.imap.org), maintained at the University of Washington. This site includes a more in-depth comparison of POP3 and IMAP, relevant RFC's, and a listing of clients and servers that currently support IMAP.