'Nessun Dorma' is a famous aria in the opera 'Turandot' and is sung by Liu, the main male character. In the story, Liu has answered the three impossible riddles the princess Turandot has always asked all her suitors and for his success he gets to marry her; if he'd failed, he would've been executed like all the other guys that'd tried before him. And the reason they all try is because Turandot is supposedly the most beautiful woman in the kingdom at least, if not the world.

Turandot has had a long record of being single and hating men, however, due to some great-aunt or whatever of hers several hundred years back being seduced, then mistreated by a lover. So she's decided to carry out some weird form of vengeance/justice. But when Liu answers her riddles and wins her hand, he says that if she can find out his name by sun-up, he'll die and she'll still be free. Yes, she didn't know his name in the first place; that's just how these stories go.

Anyway, Turandot doesn't find out Liu's name, even though she threatens to kill everyone in the kingdom to find it out. The couple has a little heart-to-heart (in opera terms this means they sing at each other for about 10-15 minutes) and Liu convinces Turandot that not all men are scum and he won't treat her badly like her ancestor had been treated. Then she does a 180 and falls for him and everything's happily ever after. The End.