Every instant the sun emits a certain amount of energy. After 1 second that energy is spread across the surface of a sphere 4pi(c)^2 big. After 2 seconds it's spread across a the surface of a sphere 4pi(2c)^2. And so forth.

Or another way to look at is that that at a certain distance from the sun all the energy leaving the sun is passing through a sphere that grows that same way.

EDIT: Thanks to grn for pointing out I was confusing the constant of a sphere's volume with its area. Fixed.