The Entrance is a room of the Gloomy Manor in Luigi's Mansion: Dark Moon. It is the first actual room that Luigi visits. This room leads to the Garage which is to the west, the Guard Hall which is north, the Mudroom which is to the east, and the Front Yard which is directly south.
During the first mission A-1: Poltergust 5000, Luigi heads through the Entrance to gain access to the Garage. After finding the Poltergust 5000, Luigi heads back into the Entrance to vacuum away an opening to the Mudroom. A Gem can be found in the Entrance in A-3: Quiet Please! Simply interact with the right knight's armor and pick up the helmet. Use the blow function on the Poltergust 5000 to shot it at the painting of a knight on the left side of the room to get the Gem.
Once Luigi competes the first mission, he will be pixelated to the Entrance for the remaining missions of the mansion, not going back to the Front Yard.