A set is a collection determined entirely by its members
A set is a collection of distinct objects, considered as a single mathematical object in its own right. The objects in the collection are called its elements or members, and the fundamental question you can ask about any proposed set is simply which things belong to it. When we write the set A = {2, 4, 6}, we mean the unique collection whose elements are exactly the numbers 2, 4, and 6. Nothing else is hidden in the set beyond its membership list. This idea is deceptively simple, but it is the foundation on which all of modern mathematics rests.
Because a set is determined by its members and nothing else, order and repetition do not matter. The sets {2, 4, 6}, {6, 4, 2}, and {2, 2, 4, 6, 6} are all the same set: they have exactly the same members. This is the content of the axiom of extensionality, the most basic law of set theory. Two sets are equal if and only if they have the same elements, no matter how they are described or listed. A roster that reads {apple, banana, cherry} and a roster that reads {cherry, apple, banana} are merely two ways of writing a single set.
Sets appear everywhere outside of pure mathematics. A database table of customer IDs is a set (each ID is distinct and order of rows is irrelevant to the data). A tag cloud on a blog post is a set of labels. The collection of courses a student is enrolled in during a given semester is a set. In every case, the identity of the collection is settled entirely by which items belong to it, and two collections with exactly the same items are the same collection regardless of how they are stored or displayed.