Ramsey's theorem is a fundamental result in combinatorial mathematics that deals with the conditions under which a certain order must appear within a structure. Specifically, it states that in any sufficiently large group of people, some subset will always have members who know each other or do not know each other, regardless of how relationships are formed. This theorem can be applied to various fields, including graph theory and computer science. It highlights the idea that complete disorder is impossible in large enough systems, leading to unavoidable patterns or structures within them.