The belt system is relatively new. Originally there were only two belts - white for student and black for instructor. When someone became an instructor they were presented with a black belt.
Judo was the first martial art to introduce the colored belts (obi) in a ranking system as a visible indication of the studentsí progress. The colored belt ranking system soon was adapted for Karate and other martial arts. Sensei Gichin Funakoshi was one of the first to use them for his Shotokan Karate schools.
As students pass through the ranks taking grading examinations they are awarded with different colored belts. The color order and which colors are used varies from school to school, as does the relationship between belt color and rank (= Kyu). However the Kyu or number/rank always starts at 10 and ends at 1. Black belts ranks start from 1st Dan and go to 10th Dan, the highest.
Ranking/belt systems and colors are selected by the governing Master(s) or Federation of a particular style, or in the case of many "independent schools (Dojos)", the head instructor. Not all styles of Karate maintain the same belt colors,
In the old days the white belt was simply dyed to a new color. Due to the dying process, it is practical to increasingly use darker colors. All of this came about shortly after the second world war, when Japan was a very poor country, and dying the belts to a new color was a cheap way to have a visible, simple and effective ranking system. Today it is much easier to just purchase a new coloured belt from martial arts suppliers.
Coloured belts image from: