Port 3389 is the primary port for Remote Desktop Protocol (RDP), which allows users to start remote sessions on servers.
Remote Desktop Protocol (RDP) is a proprietary protocol developed by Microsoft which provides a user with a graphical interface to connect to another computer over a network connection. The user employs RDP client software for this purpose, while the other computer must run RDP server software.
Clients exist for most versions of Microsoft Windows (including Windows Mobile), Linux (for example Remmina), Unix, macOS, iOS, Android, and other operating systems. RDP servers are built into Windows operating systems; an RDP server for Unix and OS X also exists (which one? Citation please). By default, the server listens on TCP port 3389 and UDP port 3389.Microsoft currently refers to their official RDP client software as Remote Desktop Connection, formerly "Terminal Services Client".
The protocol is an extension of the ITU-T T.128 application sharing protocol. Microsoft makes some specifications public on their website.