IMAP / IMAP4 - Internet Message Access Protocol (IMAP) is a standard protocol for accessing email from your local server. IMAP (the latest version is IMAP4) is a client/server protocol in which email is received and held for you by your Internet server. IMAP requires continual access to the server during the time that you are working with your mail.
Unlike POP, IMAP works more like webmail where all of your email messages remain on the remote server. Deleting email from your email client (ex. Outlook), won't delete the email from the mail server. You'll need to delete it from both your email client and the mail server (webmail), or use a function (such as Purge in Outlook) to remove deleted items from the remote server.
See the KB article "What is the difference between IMAP and POP email accounts?"