While the discovery of the golden numbers is attributed to Fibonacci, the golden ratio has been known for at least 6,000 years.

This is a good site that covers it all

The simplest way to describe the golden ratio is to explain how it is derived. I think of it as the ratio of natural growth.

The golden numbers are derived by adding the last total to the last golden number
0+1=1; 1+1=2; 1+2=3; 2+3=5; 3+5=8; 5+8=13; 8+13=21; 13+21=34; 21+34=55; 34+55=89; 55+89=144 etc.

The Golden Ratio~~1.618~~ is defined by dividing one golden number by the proceeding one in the sequence
.... 5/3=1.6; 8/5=1.6; 13/8=1.6; 21/13=1.615; 34/21=1.618; 55/34=1.618; 89/55=1.618

Golden ratio conjugate~~0.618 is by dividing one golden number with the next one in the sequence.
.....3/5=0.6; 5/8=0.6; 8/13=0.6; 13/21=0.615; 21/34=0.618; 34/55=0.618; 55/89=0.618

The Golden Ratio is also refered to as Phi.

From the golden numbers the golden spiral can be produced.
How to Draw the Golden Spiral

And here's some examples of the Golden Ratio and Spiral
15 Uncanny Examples of the Golden Ratio in Nature

Golden Ratio in Human Body

This video shows the editing a face to fit a golden ratio grid. At the end are before and after shots.
Anyone can look hot with the Golden Ratio.