This is not an easy question to answer in view of the fact that Arthur Miller was one of the greatest dramatists of the twentieth century, not to mention the fact that he wrote for over six decades. Here are some contributions.
First, Miller was a poetic realist. This might seem like an odd juxtaposition, but it need not be. For instance, Miller showed the hollowness of the American dream in his work, The Death of a Salesman. Willy Loman was a tragic figure and represented the life of many people.
Second, Miller was also able to make social commentaries in a provocative way. For example, his third Broadway play, The Crucible (1953) dealt with the Salem witch trials of 1692. This work could have been seen as a social commentary on what senator Joseph McCarthy was doing in America. In fact, Miller had to stand before the Committee of Un-American Activities in 1956. While he was on trial, he famously stated, "My conscience will not permit me to use the name of another person and bring trouble to him."