Mount Doom, or Orodruin, is a volcano in Mordor where the One Ring was forged in the Crack of Doom, a fiery chasm within the mountain. Frodo's quest to destroy the Ring at Mount Doom occupies the bulk of The Lord of the Rings.
Orodruin is Sindarin for "Fire Mountain". The Sindarin equivalent of Mount Doom is Amon Amarth, meaning "Mountain of Fate".
When Sauron chose the land of Mordor as his dwelling-place in the Second Age, Orodruin was the reason for his choice. He 'used the fire that welled there from the heart of the earth in his sorceries and his forging.' The most famous result of his forging, and in fact the only one we know of for sure, was the One Ring.
Orodruin was far more than a natural volcano - Sauron seems to have extended his own power into it, and was able to control its fires. It seems to have lain dormant when Sauron was away from Mordor, and sprung into life when his power grew.
In Peter Jackson's trilogy of movies, the New Zealand volcano Mount Ngauruhoe was used as Mount Doom in some scenes. In long shots the mountain is either a large model or a CGI effect, or a combination. It was not permitted to film the summit of Ngauruhoe because it is sacred to the Maori of the region. However, some scene in the slopes of Mount Doom were filmed on the actual slopes of Mt. Ruapehu.