Realism is the accurate depiction of both contemporary life and nature. Realism was first established by an art collective who came to prominence during their series of independent exhibitions from 1850s to the 1880s. The French painter Gustave Courbet was the key figure in the the Realist movement, and in some respects he led the movement.
Courbet's belief was to stay true and honest to what he observed and not to embellish or change what he saw when recreating it on canvas. Courbet's style of art built upon the recent work of his contemporaries, he moved away from the traditional French School of painting's practices regarding line and form. Instead seeking to show the irregularities that were present in the real world. To sum up, Realism was to depict the harshness in life, and by doing so challenge the contemporary ideas of art.
For more of an idea of what Realist painting looks like study the works of Courbet and Jean-Francois Millet; the founders of Realism.