Grand Master was a title used in both the Old and New Jedi Orders to describe the recognized head of the Jedi Order.
While this rank was recognized historically by the New Jedi Order, it wasn't until 18 ABY when Luke Skywalker officially claimed the title, upon his re-instatement of the Jedi Council. While the Grand Master was the unquestioned leader of the Jedi, both known Grand Masters (Yoda and Skywalker) still kept the Jedi Council as a source of advice.
The Grand Masters were known to be the most prominent Jedi of their era, whether through feats of valor or otherwise. They were apprenticed to the wisest Masters of their time, and had proven their prowess with lightsabers, having fought with them in the major Galactic conflicts of their day. They were known to have incredible Force potential, and were very proficient in its applications. Master Yoda, widely recognized as the most powerful Jedi in the Order, was also credited as being the greatest lightsaber duelist in the History of the Jedi Order. He trained Jedi for more than eight-hundred years, during which time every youngling in the Jedi Order received some form of training from him. Through Yoda, the foundations were laid for which future generations would restore the legacy of the Jedi. Luke Skywalker, after being trained by both his father's master and Master Yoda, toppled the Galactic Empire and through the redemption of his father brought balance to the Force. Skywalker then created a New Jedi Order in the wake of the Galactic Civil War.