George is a round character because he achieves a change in the plot as it goes. In comparison to Lennie, for instance, he is able to realize that he has hurt Lennie in the past and feels remorse for it. Although he has always maintained the same line of duty as far as taking care of Lennie, he does undergo a series of self-realizations and has been under the obligation of making severe choices that will, eventually, change his life.
First, George had to open up to the rest of the field hands against his will. He is a reserved and quiet man, and he would have never done that if it weren't to help Lennie not make a fool of himself. Second, George had to mold himself to circumstances instead of remaining flat: This is when he begins to realize the burden of Lennie and the impossibility of his dream. Finally, when he kills Lennie he knows that he is taking the risk of killing everything he ever dreamed of, stood for, or wished for. Hence, George's roundness of character is based on how destiny molds and changes him.