A playroom (also called a rumpus room or a day nursery) is typically a room in a home set aside for children to play undisturbed (and not disturbing others). They can also be found in some public locations where children are expected to be present but waiting for adults to do things.
Playrooms in homes
A playroom in a private home is typically a room set aside where it safe for children to play, and otherwise take up room with their toys. This in a larger home might be part of a nursery suite, or simply a separate room that allows for the living room to be used as a parlour for adult gatherings without having to make special arrangements or confinements for the household children. So different times and families can differing opinions and rules about playing outside of the playroom.
Homes with older or no children might instead have a game room less suited for rough housing and free form play, but which may contain special furniture such as a billiard table or dart board.
Playrooms in public locations
A playroom in a public place is normally a specialized waiting room for children. There, children can wait for their own appointments or adults to do tasks, such as visiting a doctor's office, or finishing their meals in some family friendly restaurants. Some places have actually specialized in providing the playroom and might only offer meals as a secondary function of their business.
Playrooms in an adult context
In adult, particulatly BDSM, contexts, a playroom is similar to a play dungeon where private activities can be contained to either heighten the rooms' feel or simply keep the toys contained away from less kink-aware guests. Such room are often seen as less hard core than private dungeons either in play style or dedication.