Answer:
It's called the Natural Logarithm because so many processes in nature can be described mathematically using it.
For example:
1) The population of a colony of rabbits that reproduce at a constant rate
2) The decay rate of a charged capacitor
3) The decay rate of a radioactive isotope
4) The rate at which your money will grow if you apply an interest rate continuously over a period of time.
5) The population of seeds in a sun flower
6) etc.