Premier (or premiere) has to do with things that are first, like the first performance of a play, or the leader of a country.
When a TV show premieres, it's the first episode; a movie premieres when it's shown for the very first time. An actor’s first appearance can be called their premiere. As a noun, verb, or adjective, this word has to do with a first. Leaders of countries are often called “premiers,” since they’re the first, most important people in government. Kind of like how we call the President's wife the “First Lady.”