The mountain guarded by Smaug in Jackson’s The Hobbit films is Erebor, also known as the Lonely Mountain. It is the home of the Dwarves’ Kingdom under the Mountain and the destination of Thorin Oakenshield’s quest to reclaim his ancestral kingdom.
Erebor lies northeast of Mirkwood, with the human town of Dale built near its southern slopes. The Dwarves became wealthy there because the mountain contained enormous stores of gold, jewels, and other treasures, including the Arkenstone. Smaug attacked Erebor, drove out the Dwarves, destroyed Dale, and settled inside the mountain atop the hoard.
In The Hobbit, Bilbo Baggins travels with Thorin and thirteen Dwarves to enter Erebor through a secret door. Their plan is to recover the treasure and ultimately drive out the dragon. The name “Erebor” is the Sindarin name, while “Lonely Mountain” is the more familiar English description. It should not be confused with Mount Doom, which is in Mordor and is associated with the One Ring.