This definition is from the ComputerUser.com High-Tech Dictionary:
Internet Message Access Protocol. A protocol that allows a user to perform certain electronic mail functions on a remote server rather than on a local computer. Through IMAP the user can create, delete, or rename mailboxes; get new messages; delete messages; and perform search functions on mail. A separate protocol is required for sending mail. Also called Internet Mail Access Protocol.
IMAP allows the user to read email from many different locations and accounts because email folders are stored on the server, locally, at the home or the office, for instance. Even saved and read messages are stored on the IMAP server. POP only stores new unread messages on the server, and the read and saved messages are stored locally. To force POP to not delete email once it has been read can create many copies of the same email, creating a waste of space and confusion. However, IMAP is usually more complicated to set up. If you only have one email account, POP is most likely your best choice. If you want to access more than one account, from different locations, IMAP will probably serve you most efficiently.
Cyrus has its own mailbox database which is standalone and increases performance, whereas Washington uses the stanard UNIX mailbox format, which was designed for a smaller set of users. Washington is portable to more UNIX and non-UNIX systems than Cyrus. The main difference is that with Cyrus, you don't have to add new users to your linux box (i.e. in /etc/passwd) to add new mail users, and with Washington, you do.