The cultural studies theory known as Structuralism uses a term of art called "binary opposition" to explain human knowledge and to explain how many naturally occurring phenomena are constructed. Systems are "binary" when they are composed of only two parts. It's easy to imagine things "in opposition," like the Boston Red Sox and the New York Yankees, or the World War II alliances known as the "Axis Powers" and "the Allies." For an opposition to be truly "binary," however, the opposing classes of thing/idea must be mutually exclusive. That is, membership in one class must make impossible membership in the other. The baseball teams might be thought to be binary opposites, but remember that Babe Ruth played on both teams (hence the fabled "curse of the Bambino" on the Red Sox for trading him to the Yankees). If we are using the teams to construct the system of "major league baseball" for all time, it's apparent that one can play for both teams without destroying the system or one's self. The situation in World War II also resembled a binary opposition, with membership in the Axis or Allies being sharply distinguished in most cases, but some nations belonged to neither side, like the neutral states of Switzerland, Portugal, and Spain.
True binary oppositions that organize a class of thing are not supposed to allow confusion, that is allowing a thing to claim membership in both simultaneously, or exclusion, non-membership while still belonging to the class of things organized by the binary. The most obvious place in which binary oppositions work to structure knowledge is in computers' "machine code," the most basic level of programming which tells each tiny microprocessor switch whether it is to be opened (0 or "off") or closed (1 or "on"). Everything you see on this screen, together with instructions for how it is to be displayed and where it is to be stored, is expressed to the computers in enormous strings of zeros and ones, a binary code that cannot fail if properly constructed.
The world of natural objects contains other "natural binaries," like magnetic poles (north and south) and gravitational force (to or away from the object in question). Some other binary structural principles in nature are "handedness" (AKA "chirality"--left vs. right) and symmetry vs. asymmetry. However, the more science investigates other presumed natural binaries, the more often they discover instances of confusion or exclusion. For instance, in the case of plants or animals which reproduce sexually, a naive view would imagine each species divided into binaries of "male" and "female," but hermaphrodites (both male and female characteristics) occur, as do species that change their sexual characteristics in response to environmental stress or ordinary life cycles (sea scallops). "Alive" and "Dead" used to be considered obvious natural binaries, but discoveries of objects called "prions" have called this into question--they appear to have no DNA but reproduce themselves and exhibit other life-like characteristics.
In the world of human cultural artifacts, binaries are much likely to be ambiguous if pressed to their limits, but they can function perfectly well as principles we use to navigate culture from day to day. For instance, we conventionally call "day" the period between sunrise and sunset, and "night" the remainder (or is it vice versa), although poets and painters long have drawn our attention to the beauties of the transitional moments at the dividing point between them. "Legal" and "Illegal" similarly function to help us distinguish between kinds of behavior even though a whole industry has grown up to argue the ambiguous points, and every year decisions it makes are found to be deeply disturbing to portions of the populace. In literature, we will use binaries to determine how the text's world is structured just as we would our own, but we also unconsciously use binaries to organize thematic elements, like fire and water images in "Young Goodman Brown," moon-time and clock-time in "My Kinsman, Major Molineux," and poisonous and curative powers in "Rappaccini's Daughter." Authors often construct elaborate networks of associated binary oppositions to make a large text coherent. For instance, click here to see a list of binary oppositions at work in The Wizard of Oz.