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

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.

If someone handles a difficult situation with delicacy, they handle it very carefully, making sure that nobody is offended.

A delicacy is a rare or expensive food that is considered especially nice to eat.