A factorial represents the number of ways you can organize n objects.
There is only one way to organize 1 object. (1! = 1)
There are two ways to organize 2 objects (e.g., AB or BA; 2! = 2)
There are 6 ways to organize 3 objects (e.g., ABC, ACB, BAC, BCA, CAB, CBA; 3! = 6).
How many ways are there to organize 0 objects? 1. Ergo 0! = 1.
This is consistent with the application of the gamma function, which extends the factorial concept to non-positive integers.