This phrase describes the idea that whoever is the most powerful is the one who gets to decide what is right or just.  Depending on how you view it, this is either an incredibly cynical idea or quite a realistic one. 

Consider the concept of privilege.  Privilege, whether it results from one's race, sex, finances, gender, or some other quality, confers power.  White people, to give an example, have racial privilege in the United States, and this generally gives white people more power when compared to people of color.  This means that white people are voted into public office more often than other races and that white people are most likely to become judges. 

White people, then, disproportionately make up group of individuals who make decisions about laws and punishments, and it's a fact that black people who are convicted of crimes generally receive harsher sentences than white people do.  However, because a black defendant has been given a "fair trial"—the dynamics of privilege hidden by legality—their punishment seems to be just.  Thus, "might is right" could more accurately be stated as "the mighty have the power to determine what is right."

The phrase "might is right" refers to the idea that people who have power can do whatever they want.  This idea is often phrased a little differently as "might makes right."  In this case, the word "might" is being used in the sense of power and the word "right" can mean either what is morally right or what one has the right to do.

In human terms, when the people who have the might do something, it can automatically come to be seen as morally right even if it really isn't.  This is true partly because no one can stop someone else who has a lot of power.  And it is partly true because "the winners write the history."

In the context of this story, the phrase refers to how life plays out among animals.  Among animals, whoever is strong enough to kill its food or its rivals will survive.  In such a case, there is no question about what is good or bad -- just who has more power.