Okay kiddo, you know that everything in the universe is made up of tiny things called atoms, right? And these atoms are held together by forces, one of which is called gravity.
Now, let's say you have a really big object, like a planet or a star. This object is so big and has so much stuff in it that it creates a really strong force of gravity around it. This force of gravity is called a "gravitational field" and it's what makes things stick to the surface of the planet or orbit around the star.
When we talk about "non-relativistic" gravitational fields, we mean gravity that is not affected by the theory of relativity. Relativity is a really complicated theory that only grown-ups really understand, but basically it says that time and space are connected and they can warp or bend in the presence of really strong gravitational fields.
But when we talk about non-relativistic gravitational fields, we're usually talking about weaker gravity, like the kind you feel on Earth or around the planets in our solar system. This kind of gravity is much simpler and easier to understand than the crazy gravity around black holes or other really massive objects.
So, to sum up: non-relativistic gravitational fields are the simpler kind of gravity that we encounter in our everyday lives, and they're what keep us firmly grounded on the Earth and keep the planets orbiting around the sun.