Jedi Master was a rank in the Jedi Order given to wise and powerful Jedi, many of whom were prominent leaders within the Order.
Only Masters were allowed to serve on the Jedi High Council. A notable exception this, however, was when Anakin Skywalker was appointed to the Council as a representative of Supreme Chancellor Sheev Palpatine despite only being a Jedi Knight.
In the time of the High Republic, the Jedi High Council notably consisted of three Jedi Grand Masters; Lahru, Pra-Tre Veter, and Yoda all elected to share the role. Other masters of High Republic Era included Jora Malli, Stellan Gios, Sskeer, Oppo Rancisis, Yarael Poof, and Avar Kriss.
As one of the oldest Jedi Masters in the order’s history, Yoda, over the course of his 800-year-long career as a Jedi Master, trained no fewer than 20,000 Jedi and held the position of Jedi Grand Master for over 200 years.
In the years of the Galactic Republic, the Jedi High Council was made up of twelve Jedi Masters, one which bore the title of Grand Master, who had the power to grant Jedi Knights the title of Master, in consensus. Other prominent Jedi Masters who also sat on the Council included members such as Mace Windu, Kit Fisto, Adi Gallia, Yaddle, Saesee Tiin, Agen Kolar, Even Piell, and Shaak Ti. Many Jedi Masters also took on apprentices to train in the ways of the Force, such as Depa Billaba and Luminara Unduli.
After serving as a Jedi Knight for three years, Anakin Skywalker advanced to the point in his training that he felt he deserved the rank of Jedi Master, though the Council did not agree. When Supreme Chancellor Sheev Palpatine appointed Skywalker to the Council as his personal representative, the Council reluctantly agreed, hoping to use him as a means to spy on Palpatine. However, the Council did not grant Skywalker the title of Master. Skywalker took this as both an outrageous and unfair insult, as no Jedi in the history of the Jedi Order had ever been placed on the Council without receiving the rank of Master.
Years after the Great Jedi Purge and the Galactic Civil War, Luke Skywalker attempted to train his own generation of Jedi and was considered a Jedi Master, though it was merely a role he played not having formally earned such a title until posthumously completing said role as Padawan Rey‘s mentor as a Force spirit.
Following the Battle of Exegol in 35 ABY, Rey took up the family name of her mentors Luke and Leia Skywalker. Now the last Jedi, Rey Skywalker ascended to the rank of Master.