The Jedi Order has four basic ranks: Youngling, Padawan, Knight, and Master. Although the names and specifics differ throughout the history of the Jedi, the basic progression from trainee to Knight to Master remains the same.
A Youngling or Jedi Initiate is a Force-sensitive child raised in the Jedi Temple who receives basic instruction in the Force. Younglings who pass the Initiate Trials continue their training as Padawans.
The rank of Youngling only exited from about 1,000 BBY to 19 BBY. The practice of taking Force-sensitive children as infants was intended to keep Jedi away from attachments, which would prevent them from falling to the dark side of the Force.
A Padawan or Jedi Apprentice is a young Jedi in training with a Jedi Knight or Master. In eras where the Youngling rank did not exist, Jedi trainees began at the rank of Apprentice.
When the Jedi Order was centralized, between 4,000 BBY and 19 BBY, the Master/Padawan relationship was formalized and had strict guidelines. Before and after, the process of training a Jedi was more informal; Jedi Knights and Masters had a greater choice in who they could train, could train more than one Padawan at a time, and declared their own students Knights when they were ready.
A Jedi Knight has completed training as a Padawan and passed the Jedi Trials, or similarly proven his worthiness to become a Knight.
Most Jedi are Knights and remain so the rest of their lives. Jedi Knights serve the Jedi Order by going on missions and by training new apprentices to Knighthood. Unlike the ranks of Padawan and Youngling, the rank of Knight kept its name and meaning throughout the history of the Jedi Order.
A Jedi Master is the highest rank in the Jedi Order. It is given to the most skilled Jedi after great accomplishments as a Jedi Knight, such as training several apprentices to Knighthood or performing a great service for the Republic.
Because the title of Master was so prestigious, some Jedi Knights -- particularly in the early Jedi Order -- declared themselves Jedi Masters. This was discouraged, as wisdom in the Force, not just success in battle, is necessary to become a Jedi Master.
Jedi in the Service Corps branches, such as the Agricultural Corps, are generally Jedi trainees who failed one of their trials. Although Jedi Knights or Masters could work with the Service Corps, most of their members did not have one of the four Jedi ranks.