The protocol used for managing email messages on a server is called the Post Office Protocol (POP) or Internet Message Access Protocol (IMAP). POP allows users to download emails from the server to their device, often deleting them from the server afterward, while IMAP enables users to view emails directly on the server without permanent downloads. IMAP is favored for accessing emails across multiple devices, as it keeps messages synchronized. Both protocols play critical roles in the overall email communication process.