We use the letter N to distinguish between 18-hole handicaps and 9-hole handicaps (to which we add the letter N). If you have golfers in your club with 9-hole handicaps, you should double them to correctly compare them to 18-hole handicaps.
The L and J are meant to symbolize "local handicaps." For purposes of inter-club play, the USGA sets a maximum handicap index of 36.4 for men and 40.4 for women (18.2 and 20.2 for 9-hole handicaps). Any index that goes above that number is considered a local handicap. Local handicaps are denoted with an L (18-hole handicap) or a J (9-hole handicap).
An R next to your handicap indicates that you have scored well in a tournament - so well in fact that an adjustment is made to your handicap to reflect your good performance in a tournament (the calculation is made only after you have entered several tournament scores). The R stands for "Reduced." Adjustments for exceptional play in tournaments are part of the USGA handicap formula