Pi was first described by Archimedes in the second century BC.
Pi is the ratio between the circumference of a circle (how long it takes to walk around the edge of a circle) and the circle's diameter (the maximum distance between points on opposite edges of the circle). This ratio is constant regardless of the size of a circle, and so Pi never changes.
Techniques for measuring the diameter of circles was known in Archimedes time. Discovering a method for measuring the circumference was the trick that Archimedes needed to solve in order to discover Pi.
Archimedes used a very pragmatic technique to discover the circumference of circles. He would place the circle inside of a square that was just large enough to hold the circle. He would then put a smaller square inside of the circle. The idea was to have the squares overlap with the edges of the circle at only four points. The perimeter of squares is easy to measure.
The perimeters of these two squares give upper and lower thresholds for the circumference of the circle. The circumference of the circle cannot exceed the perimeter of the larger square, nor be shorter than the smaller square.
Then, Archimedes would fit triangles between the squares and the circle. The perimeter of triangles is easy to measure. The adjusted perimeter of the squares and the triangles attached to them brought Archimedes closer to the circumference of the circle.
Archimedes would continue adding smaller and smaller triangles to fill in the spaces inside and outside the circle until the lower and upper perimeter thresholds meet. That point approximates the circumference of a circle.
Using this technique, Archimedes was able to describe Pi to two decimal places: 3.14. This number is still correct today.