Combinatorics is a branch of mathematics involved in the study of the properties of discrete structures. For example, this video explores this combinatorial problem: how many unique paths can get you from one corner of an N x N square grid to the other without doubling back? It might seem like a simple problem, but as this video shows, the complexity grows shockingly quickly. Problems like these are central to computer science and the analysis of algorithms, and as such their solutions have a major role in how the modern world operates.
There is an upcoming online course on the subject offered by Princeton for free starting March 20th offered here.