I'll take a guess, and I assume somewhere in the prize list the restrictions are stated.
Low Hunter is most likely open to any rider and horse combination. This includes Amateur or Professional riders. Some riders might use this division as a warm-up or schooling for their horses to jump in other divisions at this show with bigger jumps.
Intermediate Rider is most likely open to any horse, but there is probably a restriction on the rider; could be how high the rider is jumping at this show in other classes or has jumped at any other show, or how many blue ribbons the rider has won. Since the restriction is on the rider, I am guessing most riders will be Amateurs.
Low Children and Adult tells me that there might be a regular division of Children and Adult that jumps higher at this show. This low division is most likely restricted to Juniors and Amateurs not allowed to cross enter into other classes jumping higher than 2'6" at this show.
Remember, this was all a guess. Contact the show to be sure of the division restrictions before you enter. And good luck!
I think different show circuits have different rules, but the person above gave descriptions that are similar to the rules in my area
My show circuit also has three different 2'6" divisions -
One is for *riders* who have never shown higher than 2'6" (we call it intermediate too)
One is for *horses* who have never shown higher than 2'6" (for green horses)
And the third is open to anybody, so people use this division as a warmup or trainers can ride in it or whatever