Imagine you have a bunch of dots on a piece of paper. These dots are called "points." Now, imagine drawing lines that connect some of these points. These lines are called "edges."
A 0,1-simple lattice is when you draw lines that connect the dots in a very specific way. First, you start with a dot in the middle. Then, you draw lines that connect this dot to all the other dots that are exactly one unit away (like the dots directly above, below, to the left, and to the right of the center dot).
Next, you can draw lines that connect the dots that are exactly two units away from the center dot (like the dots in the corners of a square around the center dot). However, you can only draw these lines if they don't cross any of the other lines you already drew.
The result is a pattern of dots and lines that looks like a bunch of squares with some diagonal lines. This is called a 0,1-simple lattice!