The secret entrance to the Lonely Mountain opened on Durin’s Day is the Back Door.
The Back Door was a concealed passage into Erebor, designed as a private route into the Dwarves’ kingdom under the Mountain. Unlike the exposed Front Gate, it was hidden in the mountainside and was difficult to find without Thrór’s map and its accompanying key. Thorin’s company reaches the correct location after following the map’s instructions.
On Durin’s Day, the final sunlight strikes the mountainside at the right angle. A flake of stone breaks away, revealing the keyhole. The company uses the key to open the door, allowing Bilbo to enter Smaug’s lair and investigate the dragon’s treasure. The timing is crucial: the entrance cannot be found simply by searching the rock face.
Readers sometimes call it only the “secret door,” which is accurate in the novel’s narration, while “Back Door” is its named map designation. It should not be confused with the Front Gate, the principal entrance, or with the Doors of Durin at Moria, which belong to a different Dwarven stronghold.