The most elementary answer is that it comes up in trying to measure the circumfurence of a circle. Given a circle with radius how can we find its circumfurence? It turns out that the diameter of a circle is (directly) proportional to its circumfurence. Meaning if you double the diamter then you double the circumfurence. If you half the diameter then you half the circumfurence. Whenever you have such a proportion it tells you that is a constant number, meaning it never changes for any circle. If you take a circle and lay a rope around it and measure it and compute this ration you will get about . Mathematicians found ways how to better approximate this number and how to even prove it is irrational (cannot be expressed as a fraction). With this number we can easily now find the circumfurence of a circle. If is the radius then is the diamter. To find the circumfurence we multiply by - this constant number of ever circle and we get that gives us the circumfurence. But there are many other places in math were this number appears. What I gave you just now is the most elementary explanation.