In addition to the other very good answers here, I encourage you to think not only of the characters, but of the "groups" which the pair represent, Lennie and Curley. Rene rightly points out that Lennie "doesn't know his own strength." The overarching point here is that none of the "underdogs" know their own strength. Just as Dr. King and others in the Civil Rights movement pointed out, one day the people will "rise up" and defeat the oppressors. No one really likes Curley, not even his own wife. The working man has the power, but without coherence in revolution, the masses are doomed to failure, just as Lennie, George and Candy will be doomed. The fight scene then, is effective in showing the ways in which frustration and anger bubble just below the surface, what could happen if things don't change for the common man, and the sadness of those who continue to feel trapped by the system.
This scene is constructed to show Lenny's passivity and nature. Lenny does not go after Curley, even after Curley has attacked him, until George gives him the go ahead. Lenny is upset that he crushes his hand, because he only meant to stop him from attacking him. Lenny does not know his own strength. It also illustrates the relationship of Lenny and George, and the position of caretaker that George assumes-for example-when Lenny is worried that this will cause Lenny to lose the privilege of caring for the bunnies. George is the caretaker, Lenny the receiver, much like Candy's relationship to the lame dog.