Muley Graves is not one of the major characters in the novel, but he is a significant character nonetheless. He is significant because he helps to drive a part of the plot and because he helps to convey some of Steinbeck's ideas or themes.
An example of when Muley Graves helps to drive the plot is when he helps Tom Joad to reconnect with the rest of his family, after Tom Joad gets out of prison. When Tom gets out of prison, he doesn't initially understand where his family have gone. Muley tells Tom where to find his family and explains what has happened to them.
Muley Graves is also significant because he helps to convey the importance of solidarity and altruism. For example, he shares his food with Tom and Casey. This is an especially kind act given that Muley doesn't have much food for himself. However, explaining his kindness, Muley says, "if a fella got somepin to eat and another fella's hungry—why the first fella ain't got a choice." Here, Steinbeck is emphasizing the necessity of, and glorifying the selflessness of, co-operation and solidarity among the working classes. This is the same message which Steinbeck conveys in much of his fiction, the most notable other example perhaps being Of Mice and Men.
Muley is also a significant character because he helps Steinbeck to emphasize the desolation and ghostly emptiness of the land once it has been abandoned. He wanders this land after almost everybody else has left and calls himself "a damn ol' graveyard ghos'." This sense of ghostly desolation arguably suggests the slow death of the working classes under the merciless, dehumanizing ideology of Capitalism. Muley Graves is, in this sense, a personification of the figurative death of the working classes. Indeed, even Muley's surname, Graves, connotes death.