Colored belts represent a students progress toward black belt. Each belt represents a certain level of skill or a certain set of skills. Taekwondo does not have a uniform color order for student belts. Each school sets its own colors, color order and number of student grades. Each school also sets its own curriculum, so two students from different school with the same color belt might not know all the same kicks, blocks or forms. For example, in my school while studying for our yellow belt, we learned palm blocks, front stance, round house kick and side kick. Other schools might teach those skills at a different level, for a different belt.
All belt systems are based on the system developed by Kanō Jigorō, the Japanese founder of Judo. Kanō introduced Judo to Japan at the turn of the twentieth century. Originally, there were six student grades referred to by number. A student would begin at Grade 6 and work up to Grade 1, and then they would graduate to black belt. The black belts were divided into 9 ranks. A student would begin at Rank 1 and work up to Rank 9. Black belt ranks have been standardized, but student grades have not.
Poetically, the white belt symbolizes innocence. It's the first step on your taekwondo journey. The yellow belt represents the earth in which the roots of your taekwondo skills will grow. The green belt represents a plant growing from the earth as the student's taekwondo skills develop. The blue belt represents the sky or heaven toward which the student's taekwondo skills stretch. The red belt symbolizes danger. At this stage the student is very skilled in taekwondo. This skill could be dangerous if the student has not also learned self-control. A black belt represents maturity, a good level of skill in taekwondo, rejection of darkness and fear.