An orphanage was a place where orphaned children were cared for.
In 1965 Scotland, twelve orphans were removed from an orphanage called Holly Tree Lodge, ostensibly being taken to another orphanage, Harbour Heights, but instead they were given to the 456 by Captain Jack Harkness in return for an influenza vaccine. The orphans were chosen because they "wouldn't be missed." (TV: Children of Earth: Day Four)
The orphaned Blakely children were taken to a police station on Carthedia which also acted as a poorly-kept orphanage when the Eleventh Doctor, acting as their guardian, was arrested for a hate crime by claiming the Daleks were evil. The Doctor used the time he was given to say goodbye to the children to break down the walls with his sonic screwdriver and he and the children then fled the pursuing police forces. (PROSE: The Dalek Generation)