There are two major protocols used by Internet Service Providers (ISP's) and hosting companies, IMAP and POP3.
POP3 is what most people use when they setup their home e-mail accounts. With POP3, each time you log on to the server with your e-mail software, any new messages are transferred from the server to your computer, and then removed from the server. This works fine for many people until they decide one day to buy a laptop. Once the e-mail message is downloaded to, say, the desktop computer, it is normally not possible to access it a second time on the laptop (note: some providers have a setting that allows a copy to be left on the server).
IMAP was devised to deal with this problem. An IMAP server stores all of your e-mail messages until you delete them. Thus, you will see the same list of messages on your laptop as on your desktop as on your computer at work. The only thing that does not transfer is your address book. It is possible to have your e-mail software save a copy of your 'message store' for review when you are off-line. When you log on again, your copy will sync with the server copy.
Generally, I recommend IMAP for most users, however, some ISP's don't provide IMAP. IMAP is especially useful when several users share a joint e-mail account, such as when serving on a committee, for example.