Traditionally, mail clients (like Outlook, Thunderird) let you download all your email and read them in the mail client on your desktop. The protocol that communicates between mail client and server when you do that is called POP3.

IMAP is an alternative to POP3. You still get to read all your email in a mail client on your desktop. But, IMAP leaves the email on the server and the mail client just reads them from there. So, if you're out and borrowing someone else's computer, you can still check your email on the server using the web, because your email is still on the server.

Just find using Thunderbird ten times easier than using a web site to read email.