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 to 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.
Yoda was both a Jedi Master and Grand Master of the Jedi Order.
A Jedi Master was a Jedi Knight who had been offered a higher ranking within Jedi Order as a result of a Jedi Grand Master seeing the Knight fit for the position. Compared to a Knight, a Jedi Master had greater experience, greater readiness, and had shown their devotion to taking their next step as part of the Order: to be a Jedi Master was the next rank all Jedi Knights worked towards as part of their life-long devotion to studying the Force, but it was a long road to prove oneself worthy of the title. Upon being given the rank, the Jedi Master was able to and expected to pursue their own studies, moving forward in their experience with the Force on their own terms. In fact, the Jedi High Council outright expected all Jedi Masters to do so.
When the moment called for a serious response, Jedi Masters were expected to be serious instead of acting glib. Often groups of Jedi younglings would receive their early education in the ways of the Force under the guidance of a single Jedi Master. The younglings would then receive more direct training under the direction from either a Jedi Knight or a Jedi Master. Jedi Masters and Jedi Knights served as Jedi Generals in the Republic Military during the Clone Wars while Padawans served as Jedi Commanders.
Jedi Master Kelleran Beq
In the time of the High Republic, the Jedi High Council notably consisted of three Jedi Grand Masters; Xo 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. Ry Ki-Sakka also gained the Grand Master rank at some point.
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 800 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, Obi-Wan Kenobi, 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.
During the Clone Wars, Jedi Masters held the rank of Jedi General over clone troopers in the Republic Military.
Under the Jedi Military Integration Act, Jedi Masters and Jedi Knights were given the rank of Jedi General for the Clone Wars. After serving as a Jedi Knight for three years during the war, 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.
Following the Battle of Exegol in 35 ABY, Rey took up the family name of her mentors Luke Skywalker and Leia Skywalker Organa Solo. Now the last Jedi, Rey Skywalker eventually ascended to the rank of Master.
- The Art of Star Wars: Visions