The Jedi Order is hugely important to the Star Wars saga, so its leadership role of Grand Master, once filled by Yoda, is worth understanding. A monastic religious order dedicated to following the will of the Force, the Jedi were one of the power players in the galaxy, often working in tandem with the Galactic Republic and defined, at various points in their history, by their elemental conflict with the dark side-aligned Sith.
Already ancient by the time of the prequels, the Jedi Order had a complex hierarchy full of arcane rules established and maintained over the course of tens of thousands of years. Disputes over such hallowed matters were quite serious and were primarily adjudicated by the Jedi High Council. While their ruling was usually respected, a notable lack of adherence to tradition became problematic in Anakin Skywalker's eyes when he was denied the title of Jedi Master upon joining the Council, ultimately leading to his turn to the dark side and the undoing of the entire Order.
The title of Jedi Grand Master was held by Yoda during the time of the prequels. This was one of the two most significant positions in the organization, the other being Master of the Order, which was held by Mace Windu in Star Wars: Episode I - The Phantom Menace and Star Wars: Episode II - Attack of the Clones, and by Yoda thereafter. While the Master of the Order led the Jedi High Council, the Order's governing body, the Grand Master provided leadership to the Order as a whole. Additionally, contributing to the education of younglings was traditionally among the Grand Master's responsibilities, presumably both as a show of humility and as a way of cherishing new generations of Jedi.
In terms of claiming the title of Grand Master, there was a clearer element of election in the former canon of Star Wars Legends. In the current canon, it seems rather to be contrasted with the explicitly elected nature of the Master of the Order. There is some evidence, however, that it is not quite so straightforward either way. There were, at one point during the High Republic Era, three simultaneous Grand Masters, including Master Yoda. As it is unlikely that they were all born at exactly the same time, a subjective judgment regarding their wisdom likely factored in, meaning that Yoda was seen as exceptionally sagacious by his peers even hundreds of years before the period of his life depicted in the movies.
Titles only go so far, though, and as evinced by his training of Luke Skywalker on Dagobah, Yoda's ability to exert a sizeable influence over the shape of the Star Wars galaxy outlived any broad recognition as a Grand Master. However, given the scope and prestige of the Jedi Order during his time as their leader, it nevertheless speaks to his quality as a Jedi that he would be given the position.