Used when someone significantly alters their viewpoint, often unexpectedly. She didn't want to go, but she changed her tune when I mentioned the free food.
Pro Tip 2/3
Possible Irony
Can be used ironically if the change seems selfish or opportunistic. Once he heard there was a reward, he suddenly changed his tune about helping.
Pro Tip 3/3
Informality
An informal idiom, common in spoken English or informal writing. My brother changed his tune about chores once he wanted money for a new game.