Ibsen is often thought of as the founder of realist drama. Other playwrights who wrote in this genre include Chekhov, Strindberg, Shaw, and O'Neill. In realist drama, the characters talk in a close approximation of everyday speech. The vast majority of modern plays, TV shows, and movies are written in a similar style, though most fail to rise to the same level of social critique.
Realism shouldn't be confused with its homeboy Naturalism. Though the two styles were being developed around the same time, they have some significant differences. Basically, Naturalism was a lot more hardcore about representing everyday life exactly as it is. Naturalist plays wanted to show a slice of life exactly as it is. Characters might talk on and on about nothing in particular, the plays might have no obvious climax – just like most days are for most people.
Realism, however, is unafraid to be a little unrealistic. Think about An Enemy of the People. Sure the characters talk in a generally conversational way, but the characters certainly go on for a long time about some pretty high-minded ideas. We're not saying that real people don't talk about these things; we're just pointing out the Ibsen's characters are hyper-articulate. Very often it seems that Ibsen uses a realist framework, in order to create a forum for ideas on stage.