As the name implies, this is a style of painting that depicts the subject matter as it appears in reality, without distortion or stylization.
Realism, also known as the Realist school, was a mid-nineteenth century art movement and style in which artists discarded the formulas of Neoclassicism and the theatrical drama of Romanticism to paint familiar scenes and events as they actually looked.
Typically it involved some sort of social or moral message, in the depiction of ugly or commonplace subjects. Honore Daumier, Jean-Francois Millet, Gustave Courbet, James McNeill Whistler and John Singer Sargeant were all realists.