Examples of some famous jedi - clockwise from left: Luke Skywalker, Qui-Gon Jinn, Mace Windu, Anakin Skywalker, Obi-Wan Kenobi, and Grand Master Yoda.
The Jedi were a religious order that all have an extraordinarily strong connection with The Force. Each and every Jedi is hand-picked at a very young age, and all of them are trained throughout their youth in the ways of the Force and also in the ways oflightsaber combat. The Jedi also have a strong influence over the Galactic Republic, which some people see as a danger, particularly the CIS. Which is odd, because the CIS themselves are pretty much owned by the Sith.
The Jedi and the Sith are constantly fighting for control of their Galaxy. The majority of their wars have been of little or no interest to the League, however, on occasion there have been turning points in the balance of power. For example, around 1034 BLF the Sith Empire fell, and the Jedi established the Galactic Republic for the first time. Despite a blip in their hold of power around 4555 PLF, in which the Sith once again took control of the Galaxy, the Jedi soon rose to power once again.
The Jedi ranks are divided by experience, with Masters being the highest ranking memebers and Padawans being the lowest. Each Master takes on an apprentice which they train for ten years, and then they are promoted to Knight. At Knight status, the Jedi may take on an apprentice of his own but he is still expected to answer to his Master. Once the Jedi has himself been promoted to Master, he answers only to the Members of the Jedi High Council, and he is also allowed to begin teaching Younglings, the youngest of the Jedi.
There are many different kinds of Jedi outside the typical Padawan-Knight-Master system. Certain Jedi are given particular tasks that play to their particular strengths. Since no-one is equally strong in all areas of the Force, Jedi are assigned roles to fully utilize their strongest Force area. For example, Jedi who are particularly strong in Saber combat will be given the status of Jedi Guardian, Jedi who are particularly strong in mental powers will become Jedi Consulars and Jedi who have a blend of different Force and Combat capabilities will become Jedi Sentinels. Other roles include Healer, Librarian and Cartographer.