I've always watched Stephen Wolfram with some interest. Being neither a mathematician nor a physicist, there's only so far I can go in interpreting this work. But here's what I'm seeing. In this particular article, Wolfram is defining simple graph manipulations to create complex graphs. This is an extension of the idea that the application of simple rules over and over again can result in complex structures. In this article, the method, applied to graphs, is used to derive a number of natural laws of physics. What this means intuitively is that we can imagine the universe as formed not only of simple particles like quarks and muons and such, but also out of simple interactions between those particles. That's what I get out of this article, at least. Your results may vary.