It was originally created in 1E 221 after the exceptionally long reign of King Harald, who died at 108 years of age and outlived all but three of his sons, however over the years the Moot became permanent and acquired an increasing amount of power. By the reign of King Borgas, the last of the Ysgramor Dynasty, the Moot had become partisan and ineffective.
After the murder of King Borgas by the Wild Hunt, the Moot's failure to appoint Jarl Hanse of Winterhold sparked the disastrous War of Succession, during which Skyrim lost control of its territories in High Rock, Morrowind, and Cyrodiil, never to regain them.
The Moot has also been used in a ceremonial role. When High King Istlod of Solitude died, a moot was convened to name his son and legitimate heir Torygg as the next High King.  This took place despite the fact there being no dispute as to who should accend to the throne.
This type of Moot is more of a formality and theater than an actual meeting to choose a king. This is because the High King swears fealty to the Emperor, and as Solitude is the city most directly influenced by Imperial culture and politics, the Jarl of Solitude has served as High King for generations.
In the intervening millennium, the Moot had only been called upon three times when the throne was in dispute, and succession has never been disputed on the field of battle - even when Skyrim became part of the Empire.