When you put on airs, you act like you’re the master of something. If you wear a top hat and insist that everyone call you “sir” or “madam” while you boss them around, then you put on airs. And stop it.
To put on airs has nothing to do with the stuff we breathe. Since the 1500s, “airs” has referred to having an affected manner. It’s from the French word air, "look, appearance, or bearing." Behaving as if you're better than other people — wealthier, better dressed, or better educated — is to put on airs. Acting like you know more than your teacher is a way to put on airs. It’s also a way to get in big trouble!