The intuition here is that combinators are higher order functions which take functions and combine them together in various ways. So for a simple example "fix"

The intuition here is that combinators are higher order functions which take functions and combine them together in various ways. So for a simple example "fix" is a combinator in regular maths where Fix f = {f(x): f(x) = x for all x in the domain of f} So if f is a function or a group action or whatever, the fixed-point set of f is all points x in the domain of f such that f(x)=x. ie the points which are unchanged by x. So if f is a reflection, the points which sit on the axis of reflection. The fixed-point combinator is of particular relevance to this site because it's often called the y combinator.