Kano Jigoro, the founder of judo, introduced the colored belt ranking system in order to denote his students' rank and progress. Initially, there was no specific visible way to differentiate between yudansha (dan ranks) and mudansha (initiates who hadn't yet attained dan ranks). Kano invented this ranking system in 1883, when he awarded his students 'shodan or dan ranks'. In those times, black and while obis (sash for traditional Japanese dress) were worn with uniform kimono (a loose robe) in order to differentiate between the yudansha and mudansha.
In 1907, Kano introduced the modern gi and its modern obi, using the traditional white and black colors, though other martial art forms later adopted the custom or variation of it, and started using different colored sashes to indicate ranks. Each martial art form has its own belt color order in accordance to its rank structure. Corresponding to the rank, colors tend to progress from lightest to darkest.
The belt that signifies the beginning of training is the white belt. Since white represents purity, the belt is given to a novice learner who has no prior knowledge in this field.
The yellow belt is given to a karate beginner who has started taking control of his life, body, and environment. The colors yellow and orange symbolize sunrise and a new birth, just as a seed begins to grow, and at times, the belt is also represented by the color orange.
As the color green symbolizes the color of spring, growth as if a green plant sprouts out of the ground, the green belt is given to a student who has entered the growing process of training. At this point, the student has built up a firm foundation, and is ready to learn more advanced stages.
At times, also represented by the color purple, the color blue or purple signifies the color of the sky. Hence, the blue belt is given to students in order to remind them that they have to reach for the heavens, and so have to continue their journey with lots of dedication and hard work.
The brown or red belt which symbolizes the color of the sun and blood, is given to students when they are able to create their own techniques, and can start imitating the advanced and complicated techniques and mannerisms from the higher belts.
The highest ranking karate belt is the black belt. Since the color black can absorb all other colors, the belt symbolizes that the student has deep knowledge of all the preceding levels, and has mastered the training.
To sum up, we can say that the colors of the karate belts are the result or way of showing commitment and discipline to this form of martial arts. Hence, each belt has to be earned to be worn, and it takes a number of years to accomplish and attain the highest level of karate―the black belt.