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."