Dragonmount is a volcanic mountain west of the island of Tar Valon, located between the rivers Erinin and Luan and dominating the otherwise flat plain between the two. It is said to be perhaps the tallest mountain in the world, and is known to be several miles high at least.
It was created during the Breaking of the World, when Lews Therin Telamon killed himself after Ishamael Healed him from the insanity caused by the taint on saidin. His return to sanity forced him to acknowledge what he had done to family and friends, and in utter despair, he began channeling massive amounts of the One Power. He drew upon all that he could possibly channel, and then exceeded it, causing a bar of white-hot energy to descend from the sky. This pillar struck Lews Therin and atomized him, but also struck the ground where he had been standing. The blast, so hot as to flash-vaporize stone, tunneled into the mantle of the Earth and caused a volcanic eruption of gigantic proportions, creating Dragonmount. 
No person has ever successfully climbed to the top of Dragonmount (or at least climbed to the summit and back), and the slopes are littered with the bones of those who have attempted it. Smoke is always rising from the summit, leading to the idea that it is an active volcano, It is the tallest mountain in the Westlands, even taller than any individual peak of the Spine of the World. Its shadow just touches the city of Tar Valon each evening.
Janduin's and Tigraine Mantear's son was born on the slopes of Dragonmount, fulfilling the Foretelling of Gitara Moroso. Tam al'Thor found the baby on Dragonmount during the Battle of the Shining Walls and adopted him with the name Rand al'Thor.