The word "order" is used in a number of different ways in mathematics. Most commonly, it refers to the number of elements in (e.g., conjugacy class order, graph order, group order, etc.) or characterizes the largest term (e.g., curve order, surface order, polynomial order) appearing in a mathematical object. The words degree and rank are also often used in similar contexts, although they sometimes have subtly different meanings.
An "order" can also refer to an ordering, i.e., a particular sorting of a given set of objects.
