Once the concept for the Haunted Mansion was approved, the Imagineers began plans to make it reality. It soon became apparent that their plans had outgrown the familiar house that had been tempting DISNEYLAND guests for years. The existing house was perfectly proportioned, so the Imagineers were reluctant to expand the structure in a visible way. How could they get guests to a show building that would have to exist outside the park's berm? The answer was a stretching room!
The mysterious stretching room's purpose was to get guests to the underground show building. Once they've descended to basement level, the walk down the portrait gallery hallway takes them under the train tracks and into the underground show building where the rest of the ghostly tour takes place. The Haunted Mansion building only houses the stretching rooms.
The Florida version of the attraction couldn't be built underground due to the state's high water table, but Roy Disney felt that guests would feel cheated if the stretching room was omitted, so it was included, though the ceiling actually stretches up rather than down. The room itself goes nowhere.