The Gracie name is synonymous with Brazilian Jiu Jitsu. They are one in the same. Without the Gracies, BJJ doesn`t exist and neither does the sport of Mixed Martial Arts as we know it.
Most might not know that the UFC was created by Rorion Gracie (eldest son of Helio Gracie) to show the world that Gracie Jiu Jitsu was the most dominant martial art in a real world application. (no holds barred fighting)
Rorion selected his younger brother Royce to represent the family in the first tournament. The rest as they say, is history.
The real history began in 1917 Carlos Gracie, 14 year old son of Gastão Gracie, watched a demonstration by Mitsuyo Maeda at the Teatro da Paz and decided to learn judo (also known at the time as "Kano Jiu-Jitsu".) Maeda accepted Carlos as a student, and Carlos went on to become a great exponent of the art and ultimately, with his younger brother Hélio Gracie became the founder of Gracie Jiu-Jitsu, modern Brazilian Jiu-Jitsu.
Most people mistakenly believe that Helio Gracie created Gracie Jiu Jitsu on his own, but this was not the case. Here is a quick video by Rener Gracie explaining the origins of BJJ and the family tree. Pretty cool stuff...