Jedi that show potential and understanding of the light Virtues can advance within the Jedi Order. Such advancement brings with it more benefits, such as access to advanced combat styles and better quarters, but also more duties and responsibilities.
There are four ranks. Only the Jedi Council can promote a member of the Jedi Order to the next rank, and the council only does so when it feels the individual is ready for the added responsibilities of that rank. The exact requirements for being eligable for promotion are explained on each rank's rules page.
The Jedi ranks are: