This is your home and where you can invite other characters in the afternoon or nighttime to bond with them in order to raise your relationship status with them. Additionally, you can change your character’s hair freely in this building.
If you’re married, you’ll find your wife / husband hanging around here. New interactive events may also occur if you’re married like waking your spouse up or blowing gently on his/face after a bath.
Note: This is where the controversial "petting" mini-game was removed. In the JP version, it's known as "skinship" where you can utilize the 3DS's mic and touchscreen to interact with your wife/husband to further increase your bond with them.
Here's a sample video of that feature.