Jedi Master was a title bestowed within the Jedi Order upon exceptionally wise and powerful Jedi, many of whom held significant leadership roles in the Order.
Service on the Jedi High Council was restricted to those holding the rank of Master. However, a significant exception occurred when Anakin Skywalker, despite being only a Jedi Knight, was appointed to the Council as a representative of Supreme Chancellor Sheev Palpatine.
The rank of Jedi Master was offered to a Jedi Knight when a Grand Master determined that the Knight was suitable for a promotion within the Jedi Order. A Jedi Master possessed more experience, greater preparedness, and demonstrated a commitment to advancing within the Order, compared to a Knight. Aspiring to become a Jedi Master was the next step for all Jedi Knights dedicated to studying the Force, but proving oneself worthy took considerable time. Upon receiving the rank, the Jedi Master was then both permitted and encouraged to pursue their own independent studies, furthering their understanding of the Force at their own pace. Indeed, the Jedi High Council explicitly expected all Jedi Masters to engage in such independent study.
Jedi Masters were expected to exhibit seriousness in critical situations, avoiding flippancy. It was common for a Jedi Master to oversee the early Force education of groups of Jedi younglings. Subsequently, the younglings would receive more focused training from either a Jedi Knight or a Jedi Master. During the Clone Wars, Jedi Masters and Jedi Knights served as Jedi Generals in the Republic Military, while Padawans held the rank of Jedi Commanders.
During the era of the High Republic, the Jedi High Council was uniquely composed of three Jedi Grand Masters: Xo Lahru, Pra-Tre Veter, and Yoda, who collectively shared the responsibility. Other notable masters of the High Republic Era included Jora Malli, Stellan Gios, Sskeer, Oppo Rancisis, Yarael Poof, and Avar Kriss. Ry Ki-Sakka also attained the rank of Grand Master at some point. Yoda, one of the oldest Jedi Masters in the Order's history, trained at least 20,000 Jedi and served as Jedi Grand Master for over 800 years during his 800-year-long career as a Jedi Master.
In the era of the Galactic Republic, the Jedi High Council consisted of twelve Jedi Masters, including a Grand Master. These Masters collectively held the authority to grant the title of Master to Jedi Knights. 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 mentored apprentices in the ways of the Force, such as Depa Billaba and Luminara Unduli.
Under the Jedi Military Integration Act, Jedi Masters and Jedi Knights were appointed to the rank of Jedi General during the Clone Wars. After three years of service as a Jedi Knight during the war, Anakin Skywalker believed he had sufficiently progressed to warrant the rank of Jedi Master, a sentiment not shared by the Council. When Supreme Chancellor Sheev Palpatine placed Skywalker on the Council as his personal representative, the Council reluctantly acquiesced, hoping to utilize him to spy on Palpatine. However, they withheld the title of Master from Skywalker. Skywalker viewed this as an egregious and unjust affront, as no Jedi in the history of the Jedi Order had ever been appointed to the Council without first being granted the rank of Master.
Years following the Great Jedi Purge and the Galactic Civil War, Luke Skywalker endeavored to train a new generation of Jedi and was regarded as a Jedi Master. After the Battle of Exegol in 35 ABY, Rey adopted the family name of her mentors, Luke Skywalker and Leia Skywalker Organa Solo. As the last Jedi, Rey Skywalker ultimately rose to the rank of Master.
Tom Hoeler, an editor, has confirmed that "master" in "Jedi Master" should be capitalized when used in conjunction with "Jedi." However, the capitalization of "master" alone is not always necessary. "Master Jedi," on the other hand, is an honorific used by certain cultures or individuals, rather than a direct reference to the rank of "Jedi Master."