Acronym for Interactive Mail Access Protocol.
A modern protocol used to access MailBoxes on remote machines, designed to keep mail on the server rather than shovelling it off to the client, as POP3 would do. This advantageous for people who move around a lot: their Email is all in one central location. IMAP version 4 is in widespread use and is specified in RFC:2060. This RFC was later obsoleted with version 4 revision 1, detailed in RFC:3501.
If you want to access IMAP over a slow, laggy connection and your MailClient supports it (MozillaThunderbird does, f.ex), select all your folders for viewing offline, switch your MUA to offline mode, and just poll the MailServer for new mail as you need it. If your client does not have such support, you could try offlineimap.