Satoshi didn't explain it very well other than that he put allot of care into it. He mentions its a 64bit value, but nothing about 21x10^14 being about half the maximum representation of a positive integer by a 64bit float.

I suspect 21 was chosen based on a convergence of low risk of improper computation due to overflows when adding or subtracting two sums, and a coincidence of 7x3 which are two "perfect" numbers.

7 represents God, and 3 represents the physical universe. One could say that 21 is God's perfection manifested in the universe, or said another way; Bitcoin is condensed energy in the information realm akin to a Szilard engine