The answer to this question is one that, surprisingly, not many people can answer correctly. I mean, sure, pi is 3.141592653589793238462643... but how do you think we came up with this number? It isn't just some random output.
Here is the real answer. If you take any perfect circle, pi is the ratio of the circumference to the diameter. It's as simple as that. And if you never took high-school geometry, or haven't yet, I'll even define those terms for you. A circle's circumference is the distance around it, kind of like the perimeter of a rectangle. Its diameter is the distance across it; in other words, a line segment whose endpoints lie on a circle and that passes through the center of that circle. So pi is the distance around a circle divided by the distance through it. For a more graphical representation, view the picture below. The circumference is marked in green, and the diameter in purple.
Simple as cake - er, pi.