Jedi Master is the highest rank most Jedi can obtain. In the days of the Old Republic, it was a requirement for becoming part of the Jedi Council. It is reserved for those who have shown exceptional devotion and skill in the Force. The title of Sith Lord is on par with a Jedi Master.
The rank is usually achieved by Knights who have successfully entered Padawans into Knighthood, as it was in the days of the Old Jedi Order. The Master is then permitted to pick another apprentice. The rank can also be granted by the leading members of the New Jedi Order to a Knight for performing some extraordinary deed or service, though this is even rarer than it was in the days of the Old Jedi Order.
The rank of Jedi Master is appropriated for those who have not only showed exceptional skill in the ways of the Force, but exceptional maturity and level thinking.