In more detail
Circumference is 2πr and area is πr²: a circle of radius 5 has circumference 31.42 and area 78.54. Pi also defines the radian, the natural unit of angle: a full turn is 2π radians, so 180° = π and one radian is about 57.30°. Pi is irrational, so its decimals never end or repeat; it is also transcendental, which is why "squaring the circle" with ruler and compass is impossible.
Why it matters
Any calculation with circles, spheres, cylinders, waves or rotation uses pi, from pipe volumes to signal frequencies. Approximations carry known errors: 3.14 is 0.05% low and 22/7 is 0.04% high, fine for a garden bed but not for engineering. A standard double-precision float stores math.pi as 3.141592653589793, which is more than enough for practical work. Because area grows with the square of the radius, a small increase in diameter buys a lot of area.
Example
22/7 = 3.142857… error 0.04%
355/113 = 3.1415929… error 2.7 × 10⁻⁷
Earth's circumference ≈ 2π × 6,371 km = 40,030 km
12-inch pizza area = π × 6² = 113.10 in²
16-inch pizza area = π × 8² = 201.06 in²
The 16-inch pizza is only a third wider but has 1.78 times the area of the 12-inch one.