compliment
noun
Pronunciation: /ˈkɒmplɪm(ə)nt/
- a polite expression of praise or admiration: she paid me an enormous compliment
- an act or circumstance that implies praise or respect: it’s a compliment to the bride to dress up on her special day
- (compliments) congratulations or praise expressed to someone: my compliments on your cooking
- (compliments) formal greetings, especially when sent as a message: carry my compliments to your kinsmen
verb
Pronunciation: /ˈkɒmplɪmɛnt/
- politely congratulate or praise (someone) for something: he complimented Erika on her appearance
- praise (something) politely: the manager was heard to compliment the other team’s good play
- (compliment someone with) archaic present someone with (something) as a mark of courtesy: Prince George expected to be complimented with a seat in the royal coach

Phrases
-
compliments of the season
- used as a seasonal greeting at Christmas or the New Year.
-
pay one's compliments
- send or express formal greetings: a gentleman stopped, eager to pay his compliments
-
return the compliment
- give a compliment in return for another.
- retaliate or respond in kind: she eyed me warily, and I returned the compliment
-
with one's compliments
- used to express the fact that what one is giving is free: all drinks will be supplied with our compliments

Origin:
mid 17th century: from French compliment (noun), complimenter (verb), from Italian complimento 'fulfilment of the requirements of courtesy', from Latin complementum 'completion, fulfilment' (reflected in the earlier English spelling complement, gradually replaced by the French form between 1655 and 1715)

Compliment (together with complimentary) is quite different in meaning from complement (and complementary). See complement (usage).