POP3 is a mail transfer format that has been around for a long time, and is widely used as the default for many applications. It works by temporarily holding on a server, and your email application logs in and checks periodically for new mail, which it then downloads (and most commonly, removes the mail from the server at the same time).

So basically, in normal terms, you drop into your Post Office every 15mins and check for new mail, and take it home with you if there is any. Funnily enough, POP3 stands for Post Office Protocol.

IMAP is a newer protocol and provides many advantages over POP3. Your mail is stored on the server, all of it. I find this to be one of the best reasons to use IMAP. Frequently people mess around changing email programs, importing/exporting worrying about losing their email if they don't back up, etc. Recently I had a hard drive fail (a 3 month old 200gb one), normally getting email back would have been a major pain... in my case I just re-syncronised my IMAP folders and my mail was all there as I left it - no mess, no fuss!

Advantage number two might not be for everyone, but anyway. I run both a laptop and a desktop computer, and I want the -exact- same emails on both systems (including sent/draft folders and read/unread status), IMAP allows me to do this, and it also allows multiple connections, so my mail is always sycronised on both systems perfectly. As a bonus every single email is available via webmail should I need it. It's also a handy backup should something happen to your computer(s).

IMAP connections can remain constant, so there are no huge "waits" needed between mail being received, it also allows for a folder structure to be stored server-side for filing emails.

Downsides:
I think the advantages by far outweigh these issues, but I don't want to brush over them!
Since your email is stored on the server, it will use a fair bit of space, especially if you have a lot of attachments, so keep en eye on that (luckily most IMAP servers can tell you how much space is left).On very large inboxes (ie 1-2gb+), I have found outlook (tested up to 2007) can't cope and constantly freezes, but at that level you're probably best off using something like an Exchange Server.