Might is a word with two main meanings that show up constantly in everyday speech:

1. A way to express possibility or permission. When you say “it might rain tomorrow,” you mean it could happen but you're not certain. When you ask “might I borrow your pencil?” you're politely requesting permission. Might is gentler and less certain than words like will or must. A teacher might say “you might want to check your work” as a soft suggestion rather than a direct command.
2. Great strength or power. A knight's might referred to his physical strength in battle. A powerful nation's might includes its military forces and economic resources. When you say someone worked “with all their might,” you mean they used every bit of their strength and energy. The phrase might makes right describes the idea that whoever is strongest gets to make the rules.

The two meanings are unrelated. One is about possibility (it might happen), the other about power (the empire's military might). You can tell which meaning applies by looking at how the word is used in the sentence.