In the visual arts and literature, realism is a mid-19th century movement, which started in France. The realists sought to render everyday characters, situations, dilemmas, and events; all in an "accurate" (or realistic) manner. Realism began as a reaction to romanticism, in which subjects were treated idealistically.
Realism in visual arts: Gustave Courbet, Edouard Manet
The movement is anticipated by the work of the French author Stendhal, but the "father" of realism is generally thought to be Honoré de Balzac. His Comédie Humaine is a panoramic view of 19th-century France in over 70 novels. Gustave Flaubert clearly defined the movement with his brilliant novel of the bourgeois Madame Bovary. Balzac and especially Flaubert influenced to a high degree the later realists and naturalists: Guy de Maupassant, Joris Karl Huysmans, and, in England, George Eliot.
By 1890, many began to reject realism, thinking it too external and superficial. Modified versions, however, were employed by such authors as Thomas Hardy, who realistically presented extreme pessimism, and Henry James, who sought to understand his characters psychologically.
At the turn of the 20th century, realism as a dominant movement in France gave way to symbolism and neo-romanticism.
Realism in Philosophy
Confusingly, various philosophical unrelated positions, in some cases diametrically opposed ones, are termed "realism." In large measure this depends on which debates are active at the time, and may be encouraged by the fact that a philosophical position often looks stronger if you attach the word "real" to it.
The oldest use of the term comes from Medieval interpretations of Greek philosophy. Here "realism" is contrasted with "conceptualism" and "nominalism" (or Platonism). This can be called "realism about universals." Universals are terms or properties that can be applied to many things, rather than denoting a single specific individual--for example, red, beauty, five, or dog, as opposed to Socrates or Athens. Realism holds that these universals really exist, independently and somehow prior to the world; it is associated with Plato. Conceptualism holds that they exist, but only insofar as they are instantiated in specific things; they do not exist separately. Nominalism holds that universals do not "exist" at all; they are no more than words we use to describe specific objects, they do not name anything. This particular dispute over realism is largely moot in contemporary philosophy, and has been for centuries.
In another sense realism is contrasted with idealism'' In still a third, and very contemporary sense realism is contrasted with anti-realism
Both these disputes are often carried out relative to some specific area: one might, for example, be a realist about physical matter but an anti-realist about ethics.
Increasingly these last disputes too are rejected as misleading, and some philosophers prefer to call the kind of realism espoused there "metaphyiscal realism," and eschew the whole debate in favour of simple "naturalism" or "natural realism", which is not so much a theory as the position that these debates are ill-conceived if not incoherent, and that there is no more to deciding what's really real than simply taking our words at face value.
See also: anti-realism, legal realism, magical realism, scientific or naive realism socialist realism, fantastic realism.