A maternity ward was a section of a hospital that provided obstetrical and newborn care.
In response to the rapid reproduction of overfed tribbles in 2268, James T. Kirk jokingly suggested that Leonard McCoy open up a maternity ward. (TOS: "The Trouble with Tribbles")
The USS Enterprise-D had a section of sickbay devoted to this purpose. When Deanna Troi began going into labor with her "son" Ian in 2365, Doctor Katherine Pulaski told her they would head to maternity. (TNG: "The Child")