What it means
A goody-two-shoes is the relentlessly well-behaved one who always follows the rules, tells the teacher, never swears and makes everyone else feel like a delinquent by comparison. It's not that being good is bad, it's the smug, slightly performative virtue that grates. Said with a smirk, usually about the kid who reminded the class there was homework.
Usage examples
"Of course the goody-two-shoes handed the lost wallet straight to the police."
"Don't be such a goody-two-shoes, one bunked lesson won't end the world."
"He’s such a goody-two-shoes he actually reminded the manager nobody had signed the birthday card."
"Quit acting all goody-two-shoes, you definitely knew we were sneaking in through the side gate."
Where it comes from
It comes from The History of Little Goody Two-Shoes, a popular English children’s story published in 1765. The heroine’s nickname stuck, then drifted into everyday speech for someone who’s painfully well-behaved, morally showy, or forever playing teacher’s pet.