What Buck learns from the man in the red sweater is that the man with the club has to be obeyed. In other words, you have to do what the people with the power want you to do.
You can say that this applies to people today as it always has. Might, in some ways, makes right. We may not like it and it may not seem civilized, but at times we simply have to give in to the people with more power. If we are like Buck we can wait and get stronger ourselves and then be the ones with the power. But until we do, we have to obey.
This is partly an admission that we are weaker than someone. But Buck is also smarter than some dogs that fight to the death. Part of what he is saying is that we have to be smart enough to fight when we have a chance to win and to let it go when we don't.
The stout man in a red sweater taught Buck to respect the man holding the club. Thus, the club is not only used to inflict pain but also serves as a symbol of authority.
The lesson was driven home to Buck: a man with a club was a lawgiver, a master to be obeyed, though not necessarily conciliated.
The four men carrying the crate are afraid that the man in the red sweater will be torn to pieces given Buck’s dangerous state. However, the man lets Buck out of the crate, showing no fear. The dog lunges forward to attack but is hit by the club. Buck becomes even more aggressive and tries to attack repeatedly, but each time the club lands, causing serious pain. Eventually, Buck is struck senseless and learns the painful law of the club. The man later gives Buck some water and chunks of meat, completing the conditioning.
The lesson is also relevant to human beings because it demonstrates the need to respect existing laws and the authority of those mandated to enforce the laws. Society is also conditioned on the basis of punishment and reward. People are punished for breaking the law and rewarded when they uphold the law.