The title of Jedi Master was the highest formal rank obtainable by a member of the Jedi Order. Reserved for those who had shown exceptional devotion and skill as well as balance in the Force and often combat, only individuals who had been given the rank of Master could sit on the Jedi High Council or any of the three other Councils.
The rank of Master was a title bestowed upon very few Knights in every generation. As such, Masters made up the smallest percent of the Order's membership. The most common path to this rank was to train several Padawans as a Knight, typically one right after the other, and have them all successfully pass their Jedi Trials. If one did not wish to train several students, a Knight could choose to undergo a modified version of the Trials of Knighthood, or gain notoriety for their service to the Republic. Each of these feats could gain the High Council's acknowledgment and result in a promotion to the rank of Master. When Luke Skywalker reformed the Order following the Great Jedi Purge, he promoted his students to the rank of Master based on their degree of mastery of the Force. As the Order began to grow, most Masters were promoted based on the extraordinary deeds they preformed for the New Republic. One well known example was the promotion of Knight Kyle Katarn following the defeat of the Dark Jedi Desann at his blade.