Appliance of Science: Why do we get earworms and how can we get rid of them?

Hear there and everywhere: What to do if you get a tune stuck in your head

An earworm is music that plays in your head on repeat. 

Earworms, those little snippets of a catchy tune that gets stuck in your head and repeats over and over throughout the day. Love them or loathe them, did you ever wonder how they get stuck in your head in the first place? Or once there, have you ever desperately wondered how to get rid of them?

What exactly is an earworm?