Realism hinges on verisimilitude. The plot in realist literature may be quite interesting, but it comes secondary to the emphasis on verisimilitude -- or the desire to be truthful, accurate and real in the story. In America, this type of "real" fiction got a foothold following the Civil War and has continued to be a popular technique of writers ever since. The technique also focuses heavily on the ability to relate to the average reader. Often, the literature reflects middle-class life and is less likely to include stories that only members of the aristocracy would possibly live out. It is meant to feel real in every way even if the location and characters are complete figments of the writer's imagination.
The characters in a realist piece of literature are the primary focus of the work. Character prevails over plot every time in true realism. Developing a believable character who says things or takes the actions that seem to be consistent with his character is an important part of developing a realist piece. A realist character is highly detailed, complex and has ethics and morals that often get in the way of the action he or she must take to resolve the conflict in the story.
Drama is limited in a realistic novel and the events that take place are typically things that you could reasonably expect to happen in everyday life. There are no sensational scenes in realism unlike the romance, science fiction or naturalistic novels where anything can and usually does happen to bring the story to a close or create tension. The events in realism are always plausible and great care is taken to convince the reader that the story they are reading could potentially happen in real life.
Language is an important component of realism. If you've ever read Shakespeare and immediately pointed out that no one talks like that, then you may say the opposite about a work of realism. You'd be more likely to exclaim that you know people who talk just like that. Characters speak like you would expect them to sound based on where they are from, their education level and other factors. Spelling to help enhance the vernacular is common, and saying only the words that would normally be said in a real conversation at that time and place is also an important element.