What is the purpose of modeling in software engineering?

A model can mean a lot of things. A model is a map is anything that shows relationships in something else. A model airplane looks like an real airplane but much smaller. A model train may or may not look like a real train, but it is a demonstration of similar principles. A map is a model but has no physical resemblance at all to its subject, except to show relative distances. Here is a map from about 400 AD showing days of travel time for the entire known world: www.atlasobscura.com/articles/the-perfect-22-foot-map-for-your-ancient-roman-road-trip

In software, the concept of a map is applied to anything the computer is able to compute, so a map has no physical presence at all. A quadratic equation is a map of a baseball's flight. PV=NRT is a map of all possible conditions of an ideal gas. And so on.