IMAP (Internet Messaging Access Protocol)
A standard mail server expected to be widely used on the Internet. It provides a message store that holds incoming email until users log on and download it. IMAP4 is the latest version.
IMAP is more sophisticated than the Post Office Protocol (POP3) mail server. Messages can be archived in folders, mailboxes can be shared, and a user can access multiple mail servers. Messages are also left on the server, rather than downloaded to your terminal, like with POP3. There is also better integration with the MIME specification, which is used to attach files. For example, users can read only the headers in the message without having to automatically accept and wait for attached files to download that they don't want.
POP3 (Post Office Protocol 3)
A standard mail server commonly used on the Internet. It provides a message store that holds incoming email until users log on and download it. POP3 is a simple system with little selectivity. All pending messages and attachments are downloaded at the same time. Users who access their mail from more than one location will end up having their message downloaded to those locations, not the mail server; this is the main disadvantage of POP3.
The difference
IMAP and POP are really two different ways of sending, storing and retrieving mail. For the user, the differences between the two systems are quite transparent. Both protocols allow remote access to your mail from anywhere in the world, not just a single terminal. Attachments are allowed in both varieties. It is really down to your email software to do the hard work of encoding and decoding your messages. IMAP offers better support of the MIME specification, reducing the likelihood of some attachments not being handled properly by your software.
The main difference between the two is in how mail is stored. With POP3, messages are not kept on the mailserver; they are downloaded to your terminal. With IMAP, messages are kept on the mail server, although you have the choice to delete messages at any time.
Further information
The following links provide further details on these two protocols. They are rather technical in content, but for advanced users, provides a more indepth explanation of how they work, and how they work best for you.
Comparing Two Approaches to Remote Mailbox Access: IMAP vs. POP
Indiana University Knowledge Base: What is IMAP?
Indiana University Knowledge Base: What is POP?