The man in the beginning of this video does a good job of explaining Fibonacci sequence proportions you may find in plants. After that there is a kind of slow old documentary about Fibonacci himself.

Basically Fibonacci is said to have done an experiment with rabbits. He thought they’d reproduce in a certain way. Instead they reproduced approximately according to the Fibonacci sequence rate.

The Fibonacci sequence starts with 0 then 1. Add 0+1 and that equals 1. Then add the previous two numbers, 1+1. That equals 2. Then add the previous two numbers (1+2). That equals 3. Then add the previous two numbers (2+3). That equals 5. It goes on like this.

This what that sequence looks like: 1, 2, 3, 5, 8, 13, 21... 

Simply put this is sort of the speed at which something grows. At first it’s just 1, 2, 3, and then it starts leaping faster at approximately a Fibonacci type rate.