Part of complexity theory is understanding how algorithms perform in their worst-case scenario. An algorithm's worst-case scenario is a problem that will take a long time, or lots of resources, to solve. If people know how good an algorithm is in its worst case, they can guarantee that the algorithm will be at least that good in "every" case. People are also interested in how a certain algorithm does on average; many algorithms are very inefficient in their worst case, but are okay on most cases. Knowing how good an algorithm is on average lets people know what to generally expect when using that algorithm.