Pi is the ratio of a circle's circumference to its diameter. For any circle, the distance around is a little more than three times the distance across. That number is written π, and it does not end.
A calculator often shows 3.141592654 because the screen ran out of room, not because the number stopped. Pi is irrational: the decimal never repeats and never terminates. The usual school versions, 3.14 and 22/7, are only approximations.
NASA uses about 15 digits of π to send spacecraft across the solar system. About 39 digits would measure the circumference of the observable universe to the width of a hydrogen atom. The rest of the digits are a record of computation, not a requirement for drawing circles.
This site keeps the first 1,000,000 decimal places so you can search them. That is already far more than any measurement needs, and far fewer than the current calculation records, which are now in the hundreds of trillions.
People have estimated this ratio for more than 4,000 years. Archimedes trapped it between two fractions by drawing polygons inside and outside a circle. The name and the symbol came much later. William Oughtred used "pi" in the 1600s; Leonhard Euler's π in the 1700s is the one that stuck, from the Greek word for perimeter.
In 1761 Johann Lambert proved π is irrational. In 1882 Ferdinand von Lindemann proved it is transcendental, which also settled that you cannot "square the circle" with compass and straightedge.
To look something up in the digits, search the first million. To use π on a radius, open the calculator.