Why is an ordered pair important?

Answer 1

It is only important in the context of two dimensional coordinate geometry. If based on Cartesian coordinates, the first element of the ordered pair associated with any point gives the horizontal distance and the second the vertical distance of the point from a fixed origin.

In a radial system, the first gives the distance and the second the angle (with respect to the right horizontal line going to the right).

There are other options as well.