Webmail: Use a web browser to read your email. Emails are stored on the mail server.
IMAP: Use a dedicated email reader (Thunderbird, Eudora, Outlook Express, ...) to read mail. Emails are still stored on the mail server.
POP: Use a dedicated email reader. The emails are stored on the server until you read them. Then you store them on your computer, and they are deleted at the server. This means that you can't jump around and view mail from different computers. Well you can, but each mail will only be visible on the computer you first viewed it on.
On the other hand, you can view all your old emails even if you're offline. You won't have to bother about any email quota, since it's your HD size that gives the limit. And you don't need to worry about your provider closing your account and deleting your emails, by accident or from inactivity.
Interesting though that an email service that is mostly known for its huge quota, enables a method where you don't store anything on the servers (except unread mail). Are they running out of disk?