Fig: to make someone have a humbler opinion of himself/herself

They are still very young and after their last string of successes, they are getting cocky. It's good to take them down a peg or two

Sono ragazzi molto giovani e dopo l'ultima serie consecutiva di successi si stanno montando un po' la testa. Sarebbe bene fargli abbassare un po' la cresta

As arrogant as they are, they thought they were an unbeatable team, but the last, humiliating defeat took them down a notch or two

Arroganti come sono, pensavano di essere una squadra invincibile, ma l'ultima, umiliante sconfitta gli ha fatto abbassare le ali

Matthew thinks he's really something, but he's just a pompous ass who needs to be taken down a peg or two

Matteo crede di essere chissà chi, ma è solo un pallone gonfiato che deve abbassare le arie

Diana is much too arrogant and full of herself. Let's show her a thing or two, tell her a thing or two, bring her down a few pegs and see if she can still be so high and mighty

Diana è troppo arrogante e presuntuosa; facciamogliela vedere noi! Gliene diciamo quattro, le facciamo calare le arie e vediamo se sarà ancora così altezzosamente superiore

Probably this expression originally referred to a ship's flag. Ship's flags were raised or lowered by pegs: the higher the position of the flag, the greater the honor. So, in a figurative sense, Take someone down a peg (or two) means to lower the esteem in which that person in held