Most people could tell you that π equals about 3.14. But there is so much more to it than that!
Of all mathematical constants, π is the most well known, for good reason. It shows up just about everywhere once you start looking for it, and even when you aren't. If you are doing something with circles, π will almost certainly be there. If something is repeating (like sine and cosine), there's a good chance you'll find π.
Typically, π is defined as the ratio between the circumference and diameter of a circle. This value, circumference divided by diameter, is the same for every circle, regardless of size or position. That's what makes π a "constant".
Again, most people can tell you that π is equal to circumference over diameter. But where does it really come from? Why does that always give the same number?
The first ever real attempt at approximating π was done by Archimedes, now called "Archimedes' Polygon Approximation." There are many others now that are able to calculate millions of digits in seconds, but Archimedes gives a fairly intuitive way of calculating it.
For more information on Archimedes' Polygon Approximation, see this article by Nick Craig-Wood. You can use this visual (below) to play around with the approximation.
The generic answer is that π has to do with circles, and circles are pretty common. But there is a lot more too it than that! Yes, π is defined by circles, and yes, usually when we see π, we can also find circles. But π shows up for other reasons as well! Sometimes (actually pretty often) you will find π in the solution to a problem but maybe it isn't clear why or how you got there. In this case, walking backwards and trying to prove the solution a different way will often give you a better understanding of where π came from this time. For a great example of this, I suggest watching this 3Blue1Brown video about π in prime numbers.
With π being one of the most famous numbers of all time in math, you'd expect us to know a lot about it. And we do! Here are some things we know about π, along with resources talking more in depth about it.
It might surprise you, however, that π can still be a mystery to us. There are actually a lot of things we don't know about it, even though it seems like maybe we should. Here are some things we don't know:
It's true that π is pretty far from everyday calculations. On most days, I don't ever have to find the exact circumference of a circle from its radius. In fact, even the most critical of systems like GPS only require a handful of digits to be useful. That being said, π is still important to know about. There are so many things that we use daily where we don't think about the calculations with π going on behind the scenes. Even something as simple as a flower in nature involves π.
Beyond even that, there is still value in learning about something relatively abstract like π or math in general. Mostly, learning about π is a pathway into complex math and interesting knowledge. If you learn to love math because of π, it can introduce you to a wealth of information that you may benefit from.