Gichin Funakoshi never graded. In those days you were either a white belt or black. Either you were proficient or you weren't!
Masatoshi Nakayama was virtually single handed in popularising karate to the degree we have today. He was instrumental in having a similar grading system to that of Judo and to retain younger students realising that freestyle and competition was a necessary part of the early years in our training. The idea of gradings and of coloured belts was taken from Judo. Originally after white belt came yellow, after three gradings. Next came green, purple, brown then black.
If you follow the colours through logically you could keep the same belt and just keep dyeing it a deeper colour. This is as it was when Sensei Kidby began training except with the addition of white stripes for 4th, 2nd and 1st Kyu's. Over the years this has changed to include every colour of the rainbow depending upon one's style and association.
The idea of a silk black belt, rather than the cotton one usually worn by shodans, is that the more and the longer it is worn the whiter it becomes. The philosophical meaning behind this is simple, “No matter how good you think you are, or even appear to be, you are still a beginner on the inside”.
CFTS belt grading system (including intermediate grades for under 14's)