The umbilical connect port was a connection port on a starship which was normally used while in spacedock during repairs or upgrades. An umbilical line at the station would connect with this port to perform whatever work needed to be done.
Galaxy-class starships also had these ports on the dorsal surface of the secondary hull. There was more than one of these ports on the 'spine' of the hull. The location of these ports was labeled on a schematic of the USS Enterprise-D that was seen on William T. Riker's bridge console. (TNG: "New Ground")