The article discusses how matrices can be classified as $k$-nonnegative based on certain criteria. The researchers found a way to describe $k$-nonnegative matrices using a set of generators and relations, focusing on cases where $k$ equals the matrix size minus one or two. They showed that $k$-nonnegative matrices can be grouped into cells based on how they are made up of these generators. These cells have a specific structure that relates to how they are put together, similar to puzzle pieces fitting together. In particular, for matrices where $k$ equals the size minus two, these cells form a specific type of shape called a CW-complex.