[1] This terminology is used mainly in the "International Standard" group of ballroom dances.
[2] "Natural turn" and "reverse turn" are names of syllabus figures in waltz, Viennese waltz, foxtrot, quickstep.
In addition, the words "natural" and "reverse" are used in some other figures that amount to turning to the right or left, respectively, e.g. natural twist turn in tango and foxtrot.
In a standard ballroom closed dance position the partners are somewhat shifted to the left with respect to each other, which makes the right turn easier.
[3][4] The second reason is related to progress around the floor along the counter-clockwise line of dance.