1) N-UNCOUNT Delicacy is the quality of being easy to break or harm, and refers especially to people or things that are attractive or graceful.

...the delicacy of a rose.

...a country where the feminine ideal is delicacy, slimness and grace.

2) N-UNCOUNT: usu with supp If you say that a situation or problem is of some delicacy, you mean that it is difficult to handle and needs careful and sensitive treatment.

There was a matter of some delicacy on which he would be grateful for her advice...

He sensed the delicacy of the situation.

3) N-UNCOUNT: oft with N If someone handles a difficult situation with delicacy, they handle it very carefully, making sure that nobody is offended.

Both countries are behaving with rare delicacy...

He's shown considerable delicacy and tact in feeling the public mood.

sensitivity, tact
4) N-COUNT A delicacy is a rare or expensive food that is considered especially nice to eat.

Smoked salmon was considered an expensive delicacy...

We were served course after course of mouthwatering local delicacies.

English dictionary. 2008.