Originally, there were no belt grades in karate because karate was practiced in small groups where everyone knew each other's level. The grading system was introduced as the number of practitioners increased.
The grading system in karate is structured so that each grade contains a syllabus. In order to acquire the next grade, you must pass a graduation in that syllabus. Before you can graduate in the next syllabus, it is a requirement that you have passed the graduation in the previous syllabus. This means that you cannot be taught e.g. black belt techniques until you have achieved the degree before (1st kyu, see the structure of the degree system below). The reason for this is not only to ensure that the student has the necessary technical skills, but also that the student is mentally prepared to handle potentially dangerous techniques and not abuse them.
The structure of the degree system in Jundokan:
Kyu degrees are student degrees, starting with 10th kyu and ending with 1st kyu.
After 1st kyu comes 1st dan, which is the first black belt rank.
There is a technical curriculum up to and including 6th dan. From 7th dan and up, there are honorary degrees.
From 10-4th kyu, a minimum of 3-6 months must pass between each graduation.
From 3-1st kyu and 1st kyu-1st dan it takes one year.
Between 1st and 2nd dan, a minimum of two years of training is required. Between 2nd and 3rd dan, three years, etc.
It takes about 5-6 years to become 1st dan.
No Dane has achieved the 10th dan in goju-ryu yet, but to reach the 6th dan level you typically have to train for 25-30 years.