Things that are elementary are simple or not very advanced, as in elementary school or Sherlock Holmes' famous line, "Elementary, my dear Watson!"
Remember elementary school? That's an earlier, less advanced type of school than middle and high school. Things that are elementary are simpler — easy enough for a first grader to handle. A puzzle that's a snap to solve could be called elementary. We can also say that something is elementary when it's a basic building block of something else: a good breakfast is elementary to healthy nutrition, for example.