One of the key characteristics of Literary Realism is its use of realistic details for its setting. This means that if you write a story about the Fraser Valley in the 1850s, you would need to include details about the fashions of the time, about people's habits, and about the everyday experiences of your characters. However, this accuracy can also be pushed beyond the limits of normal reality; stories about realistic treatments of magic or mythology could be considered works of literary realism.
Unlike other styles of writing, literary realism focuses on characters that you could meet on the street on any day. These characters are described as being a part of their setting in their appearance, clothes, and habits. Also, the motivations and work of these characters will not be outlandish or extreme; a villain in a realist story would not be bent on conquering the world, and a hero could not be a person who works on magical research.
One of the major purposes of literary realism is to call into question the idealism of romanticism. Realism does this by presenting its characters with difficult moral choices, the solutions to which have consequences and limitations that are based in reality. For example, in a story demonstrating realism, a hero could not call up superhuman strength in order to pull a beached whale back into the ocean but would have to decide to do something less satisfactory.
Literary realism is not limited to story and characters, but even extends to what characters say. This everyday diction is used to help a story feel more like something that is based on a real situation or experience, rather than being a product of pure imagination. Excellent examples of this sort of diction can be found in Mark Twain's "Huckleberry Finn," where he famously writes in the dialects found in his Southern states' setting.