And a delicate topic, or a delicate conversation, must be handled with care and skill so that no one gets upset. For example, very sad news must be given to people delicately. It would be indelicate to tell your sibling, "Hey, guess what? Our dog just died." Instead, be delicate: say, "Listen, I have very sad news. Fifi passed away this morning in his sleep."
Delicate topics, like death, can easily make people upset, and delicate feelings are easily hurt. If your feelings are delicate, then you cry easily and often.
Finally, you might call something delicate if it seems lovely, beautiful, or made with skill, especially if it has many small parts or pieces. It took skillful hands and an artistic eye to make these delicate braids!