"Napoleon is always right" and "I must work harder" are the two mottos that Boxer adopts in the story.  

Those two mottos tell the reader a great deal about Boxer's character.  The first motto indicates that Boxer is through and through a blind follower.  He is not a leader by nature.  Boxer assumes that Napoleon is smarter than him; therefore, Napoleon is always right and should be always followed.  Inherent within Boxer's logic is the concept that Napoleon has everybody else's best interest in mind as well.  That couldn't be further from the truth.  Napoleon cares most about Napoleon and keeping himself in power.  

The second motto shows that Boxer is a hard worker.  There is nothing wrong with that.  A lot of people would do well to have such a motto.  Boxer's problem is that he assumes his harder work will always better benefit himself and everybody else equally.  That's because he assumes that Napoleon is always right and is looking out for everybody else as well.  Boxer does indeed work harder, but his lot in life never improves.  His harder work always goes to benefit those chosen few that are in power. 

After the Animal Farm is established, Boxer adopts "I will work harder!" as his "personal motto." After Napoleon takes over, drives out Snowball, and sets himself up as dictator, Boxer adds "Napoleon is always right," to his motto of "I will work harder."

Both mottos show that Boxer, faithful and good-hearted, is a true believer in the cause of Animalism. At the point that Boxer adopts "I will work harder" as his motto, Animalism is still working as an ideal that benefits everyone. Boxer's motto inspires him, and that inspiration motivates the other animals to work harder too and to believe that the seemingly impossible can be accomplished. Boxer, in this context, is a good role model, showing the other animals that they can work together to accomplish goals.

After Napoleon takes over, however, and corrupts Animalism to benefit the pigs alone, Boxer's motto that Napoleon is "always right" becomes a hindrance. The other animals look up to and respect Boxer, so when he throws his weight behind Napoleon, this tyrannous pig becomes much harder to stop in his quest for power.

Boxer represents the Communist who was a true believer in the ideals of the cause, helping others to work together for the common good. Such as person was an inspiration until the system became corrupt. After that, the true believers' blindness to what was going on and unthinking support of tyranny—such as in the case of Stalin—became a problem that helped perpetuate evil.

Boxer has two mottoes.  They are "Napoleon is always right" and "I must work harder."  Both of these mottoes show Boxer's role in this story.

In this story, Boxer's role is like that of the ignorant working class in Russia.  He is blindly in favor of what Napoleon (Stalin) is doing.  He feels that if he would only work harder, everything would be okay.

This shows that he has really bought in to the propaganda that Squealer and Napoleon are putting out.  He has bought into the idea that Napoleon is perfect and that the animals should work their hardest to do what Napoleon tells them.