Real Dictionary

delicacy
If someone handles a difficult situation with delicacy, they handle it very carefully, making sure that nobody is offended.
countable noun: A delicacy is a rare or expensive food that is considered especially nice to eat.
uncountable noun: Delicacy is the quality of being easy to break or harm, and refers especially to people or things that are attractive or graceful.
uncountable noun: 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.

delicacy in American English
the quality of being delicate as in taste, odor, or texture
noun: fineness of texture, quality, etc.; softness; daintiness

delicacy in British English
noun: fine or subtle quality, character, construction, etc