The check-raise is checking so your opponent bets and then raising over the top. It sounds sneaky, and that's why it works: it's one of the most powerful plays from out of position.
For value
You check with a strong hand (a set, two pair), let your opponent bet, and raise to build a big pot. You pull chips from them that they wouldn't have put in if you bet first.
9♥
8♥
5♣
As a semibluff
You can also check-raise with a strong draw (flush + straight draw). You don't need the best hand right now: either your opponent folds, or you complete your draw and win big.
💡 Don't only check-raise with monster hands: you become predictable. Mix in semibluffs to be impossible to read.
🎓 Lesson: the check-raise→