RE: Why is the earth round?
The premise of your question is incorrect. The earth, like all other observable planets, is not flat; it is an oblate spheroid, meaning it is mostly spherical but slightly flattened at the poles and bulging at the equator. This shape is caused by the force of the planet's rotation. Planets form round as their gravity pulls in everything equally from all sides.
As for the importance of this shape in programming, spherical coordinates (longitude and latitude) are often used in geo-spatial algorithms, mapping software, and to represent 3D space like in video games or simulations. Knowing the true shape of the Earth (and other planets) is critical to achieving accurate results.