IMAP4 (Internet Mail Access Protocol version 4) is a more advanced protocol than POP3. With IMAP4 your mail is stored and manipulated on the mail server.
So, if you move a message from one folder to the other, the message is moved on the server. If you send a message, your mail client will (usually) put a copy into your 'Sent Items' folder. If you delete a message, it is deleted from the server, and so on.
This has several advantages: