"Might" is a word that indicates power or strength. In this context, this is what the author tries to indicate by using this word. By claiming that "might is right," the author implies that in a society without a Constitution, a person's power would give him the right to act in a particular way. This would mean that powerful people would dominate and oppress less powerful people.
This is the situation that the Constitution wants to avoid. The Constitution states that all people are equal. This is the case regardless of whether a person is powerful, popular or rich. Moreover, the Constitution establishes a basic standard of behaviour that everyone needs to follow (no one is above the law). Therefore, the Constitution is important because it helps a society achieve an even playing field.