In the past I used to understand it in some kind of way. But it doesn't make a lot of sense sometimes. In high school, we usually take examples where the object is placed in an incline and the Normal force is equal to mg cos theta where theta is the angle of the incline. It should equal to that because it doesn't mention anything about vertical acceleration if we use the standard axes. However, I try to solve a bit more complex problems such as wedges and stuff. I usually treat normal force as a force that changes and becomes the way that I want it to be. As for example, If an object is placed on an incline and the incline (faces the left) has an acceleration to the left. We usually say that the normal force is bigger in magnitude than gravity because I believe that the incline and the object are much more compressed so there is more repel forces between atoms. What really bothers me is how do we ensure that the normal force will be like that in real life? It might be a bit confusing, but If you see it from my point of view you might know what I am talking about. The opposite will happen if the incline is moving to the right.