POP-vs-IMAP

There are three different paradigms for accessing remote message stores (or "mailboxes"). They are: offline, online, and disconnected.
offline: operation, the mail client program, or "mail user agent", fetches messages from a mail server to the machine where the mail program is running, and then deletes them from the server (this is what POP does, but is also supported by IMAP).
online: operation, messages are left on the mail server and manipulated remotely by mail client programs (IMAP only).
disconnected: operation, a mail client connects to the mail server, makes a local "cache" copy of selected messages, and then disconnects from the server, later to reconnect and resynchronize with the server (Disconnected IMAP).

In both online and disconnected access modes, mail is left on the server, which is important when people use different computers at different times to access their messages. If one's only requirement is for offline access, then IMAP is overkill.

Disconnected IMAP is different from IMAP. It synchronises what is on the server with the client, but the stuff stays on the server. So now both the client and server have identical copies of the data. Then you can change stuff locally without a connection to the server such as deleting mails or moving mails between folders. When you are connected to the server, you can synchronise the mail again: all your changes are uploaded to the server. All changes on the server that happened in the mean time, such as new mail arriving, are synchronised with the client. After the synchronisation, both client and server are identical again. This is unlike POP3, where you get your mail once, and then delete it from the server.

References on POP vs IMAP