the meaning of heuristics in artificial intelligence
Heuristics typically have very little to do with rigor. (But you can surely study them in a rigorous way). They are rule of a thumb methods for solving (usually computationally difficult) problems, and typically they perform quite well in practice. In other words, there might not be any formal guarantees on the solution quality you get by running a heuristic, but experience and empirical analysis shows they can be quite effective. Arguably, it is rarely the case we understand their behaviour well.

Sometimes, when heuristics are analyzed formally, they turn out be to approximation algorithms. That is, methods for solving a problem with a formal guarantee on the solution quality. For example, one might have observed a heuristic usually works well, and an analysis proves it will always give a solution which is at most twice the optimum. 

Perhaps in your particular case, the section "Heuristics" contains explanations (more or less formal) as to why the heuristic behaves or is expected to behave in certain ways when run.