From the Super Mario Wiki
The Dungeon Cells are a location in Treacherous Mansion in Luigi's Mansion: Dark Moon. Accessible via the Haunted Catacombs and located deep underneath the mansion's basement, they're the final room explored in the first mission.
The Dungeon Cells are a set of jail cells accessible from a long corridor. The part near the entrance has some steps leading down to an area with barrels and a Strong Hider, and the west side leads out onto another part of the cliff outside the mansion. The cell nearest the entrance has a plant and a wall that can be broken to reach the next cell, the one past said wall has some barrels and possibly a painting of a bomb, and the final cell has a chain, a painting of a bomb and a suit of armour playing checkers.
During Front-Door Key, the Dungeon Cells are the final room Luigi has to explore when looking for the missing Polterpup, as well as the location in which the key to the front door is finally recovered.
In the other missions aside from Terrifying Invasion, the Dungeon Cells are inaccessible along with the rest of the basement.