Which of the words should I choose when I ask about the meaning of a word that I don't know exactly but I know that the word I am asking about is an animate being?
What/who is a king?
What/who is a fairy?
When asking about the meaning of a word, the concept of the word is the object, not what the word represents. As such, you use "what". In your examples, you know that kings and fairies are animate beings, but you're not asking "who (among a group of people) is a king/fairy", you are asking "what (is the meaning of) a king/fairy".
Who (or the objective form, "whom") is used when you are referring to a specific person or group of people (e.g. "Who is the Queen" if you are looking to find out about the person ruling a country [the answer to the above question is "Elizabeth"]). If you are looking to understand more about the definition of "Queen," then you would ask, "What is a queen?"