Tolkien’s One Ring must be destroyed in Mount Doom. The volcano, also called Orodruin in Tolkien’s invented Elvish language, stands in Mordor and is the place where Sauron forged the Ring.
Because the Ring can be unmade only in the fire that created it, destroying it elsewhere is impossible. This makes Mount Doom the destination of the quest in The Lord of the Rings. Frodo and Sam reach the volcano after crossing Mordor, while Gollum follows them.
At the Cracks of Doom, Frodo claims the Ring rather than willingly casting it away. Gollum bites off Frodo’s finger, falls into the chasm, and takes the Ring with him. Its destruction causes Sauron’s power to collapse and changes the course of the War of the Ring.
Mount Doom is not the same as the Lonely Mountain, the location associated with Smaug in The Hobbit.