Courbet is important because he is considered the father of the Realist movement. He was one of the first artists to reject the romantic idea of painting the fantastic and dramatic and he paved the way for the more observational work of the Impressionists.
The eNotes/Wikipedia page on Courbet says the following:
Courbet occupies an important place in 19th century French painting as an innovator and as an artist willing to make bold social commentary in his work.
Courbet painted very ordinary people. He rejected the historical scenes and dramatically beautiful mythological figures that the Romantic movement was all about. He painted poor, working class people because these were the people he saw around him. It was widely thought that the plain people he represented didn’t deserve to be captured in painting form. Also, the Middle class of the 19th century saw the working class as dangerous, so Courbet’s work was not generally accepted. He was even shunned at the Paris International Exhibit in 1855 due to this aspect of his work, but he opened his own gallery space outside the grounds. He called his exhibit the Pavilion of Realism thus championing the new movement.
Courbet believed that it was the artist’s responsibility to paint only what he could see and to capture only subject matter that was relevant to his time. He paved the way for the Impressionists who took the theory of realism even one step further, focusing specifically on the accurate depiction of observable light.