"Bagger Vance" and "R. Junuh" are representations of Bhagavan (Krishna) and Arjuna, from the Hindu text "The Bhagavad Gita". The lessons learned by Rannulph are loosely based on those Krishna teaches to Arjuna while masquerading as his lowly chariot driver.
Originally, the lead roles were going to be played by Morgan Freeman and Robert Redford. But, after careful consideration, Redford decided that the movie would work better with younger men playing Rannulph Junuh and Bagger Vance.
The trivia item below may give away important plot points.
The scene in which Rannulph's ball moves and the officials are trying to get him to say it was a trick of the light or that he imagined it, is based on an actual incident that involved Bobby Jones and Walter Hagen. In 1925 Jones was challenging for the U.S. Open Championship at Worcester Country Club in Worcester, MA. On the 11th hole, as he addressed his ball in the rough, it appeared to move. It was determined that no one else saw the infraction, including his fellow competitors Gene Sarazen and Hagen, and the marshals left it up to Jones as to whether a foul should be called. Jones called the breach on himself and, after the marshal announced the stunning act of sportsmanship to the crowd, Jones replied, "Do you commend a bank robber for not robbing a bank? No, you don't. This is how the game of golf should be played at all times." He eventually lost the U.S. Open by one stroke.