The illustration is explaining switch paths based on inputs/outputs in parallel. The graph is organized into a matrix that could have anywhere from M inputs and N outputs based on the use case of it. Each of the 'dots' is a switch where an input m and output n are matched and closes this relation by noting a dot at the cross point of it.
I think that the crossbar illustration is trying to show us a lower level interpretation of how a switch handles incoming transmission and how they are sent out to their end destinations (if known). Then this idea is followed up by a 'better' way to do it used more efficient switches that can handle high memory load and more parallel connections to occur without bottle-necking.
