The first key to Gestalt is the idea of figure and ground. Basically, we naturally separate objects from their surrounding area, drawing lines around the object (figure) to distinguish it from the ground (background). This is even the case with two-dimensional objects, like most designs.
Printed words are actually great examples of this. When you look at a word, whether on a page or on a screen, you see the darkness of the letters and not the white around it, though both are completely legitimate things to look at. Your mind automatically separates the figures (the letters) from the ground (the page).
Sometimes figure and ground relationships can shift as you notice the details of them. In these classic examples, what you see depends on what group of things you see as the figure and which as the ground.