The golden ratio is a kind of a line which has a close relation to Fibonacci Numbers. It is found when the line is cut into two unequal parts, and the large part divided by the smalest part is the same as the whole line divided by the larger part.
If the line is XZ, and it is cut at Y, Then there will be a golden ratio when:
The relation to it and Fibonacci Numbers is very big. One is that the ratio of two Fibonacci Numbers is very similiar with a difference of one to the Golden Ratio's value, which is approximately 1.1680.
In a "golden spiral" which is just another shape like the Golden Ratio, the spiral is made of a set of 90* arcs. Each of these Arcs have radii as Fibonacci Numbers.
It's really complicated and there's much more to it. I've just roughly given something here.