A well-ordered set is a type of set in which every non-empty subset has a least element. This means that for any group of elements you choose from the set, you can always find the smallest one according to the set's ordering. Well-ordered sets are important in mathematics, particularly in set theory and ordinal numbers. An example of a well-ordered set is the set of natural numbers 0, 1, 2, 3, .... In this set, any subset, like 2, 3, 5, has a least element, which is 2. Well-ordered sets help in understanding concepts like ordinal numbers and transfinite induction.