What is universal computation, and why does it matter here?

Universal computation means a system can, in principle, emulate any other computer or program given the right input — the same notion behind a Turing machine. The Principle of Computational Equivalence claims that almost any process which isn't trivially simple reaches this maximal level of power, so there is no broad middle ground between "obviously simple" and "as powerful as anything." In the model, this is why even a tiny rewriting rule is taken to be capable of generating arbitrarily rich behaviour; note that universality of generic hypergraph rules is conjectured, not proven.