According to Wikipedia, IMAP (Internet Message Access Protocol), together with POP is one of the most popular protocols for email retrieval.
The setup described here enables you to store all your email (and email for other people) on a single machine, which might be a home server, a remotely hosted server, or even a desktop, and then access it from anywhere.
OfflineIMAP allows you to read your email while you are not connected to the Internet. This is great when you are traveling and really need an attachment from a message but cannot connect to the Internet.
Gmail's IMAP support is one of the biggest things to hit the webmail world since, well, Gmail. We've already covered how to use imap from Outlook, and now it's time to show everybody how to use it from the open-source Mozilla Thunderbird email client.