Harry looked over at the Slytherin table and saw a horrible ghost sitting there, with blank staring eyes, a gaunt face, and robes stained with silver blood. He was right next to Malfoy who, Harry was pleased to see, didn't look too pleased with the seating arrangements.
"How did he get covered in blood?" asked Seamus with great interest.
"I've never asked," said Nearly Headless Nick delicately.
-- Harry Potter and the Sorcerer's Stone
When I come across this word, delicate, it’s not easy to choose proper meaning from dictionaries. From his ruff, I can imagine his attractive appearance; from the situation, a careful way of speaking. What does the word mean?