The nursery was one section aboard Federation starships, such as the USS Enterprise-D. In the decades of the past, such as the 19th century, the word was used as the term for a room or suite of rooms at the top of the house made to quarter a family's children (the nurse, or nanny as she would later be known, would be quartered in an adjacent room to be within earshot of the sleeping children during the night); by the 21st century, it became known as the term for an infant's room.
Prior to Jake Sisko's birth in 2355, Benjamin Sisko became obsessed with making a nursery for him after he and Jennifer Sisko decided to conceive him. It turned out well, especially the starscape on the ceiling, which Jake adored. (DS9: "Explorers")
The Juarez baby, born in 2367, slept in a small bed in the ship's nursery, attached to sickbay, shortly after he was born. Captain Jean-Luc Picard paid the latest member of his crew a visit shortly after the boy was put to bed by a nurse. (TNG: "Data's Day")
In 2376, a rumor circulated aboard Voyager that half the crew on deck five had gotten pregnant based on Tom Paris's glancing at a monitor that displayed generational projections. Neelix asked Commander Chakotay for permission to turn Cargo Bay One into a nursery. (VOY: "The Voyager Conspiracy")