The original of something (like a recording) is the master. Masters are also experts in fields, from karate to painting.
Master actors are brilliant actors: they've mastered the skill of acting: maybe they have a Master of Fine Arts degree. It takes a long time to master anything. The master is the head of a school. People with servants, pets, and (during a horrible period in our history) slaves were called masters. A master key opens many doors, and when you master something, you are extremely good at it. An A+ on a test shows you mastered the material.