The noun society refers to people living in social order. Unless you are a reclusive person, you are a part of society in some way or another.
Society can also refer to fashionable elite, the "beau monde" or "smart set." An organization or club formed around a common interest is sometimes also called a society. To add to its mystique, this type of society might create special rules, greetings, or handshakes. Certain national societies that may have branches in your community include the Elks Lodge or the National Association of Professional Women.