If someone is mysterious about something, they deliberately do not talk much about it, sometimes because they want to make people more interested in it.
"the new insurance policy is written without cryptic or mysterious terms""a deep dark secret""the inscrutible workings of Providence""in its mysterious past it encompasses all the dim origins of life"- Rachel Carson"rituals totally mystifying to visitors from other lands"
2. having an import not apparent to the senses nor obvious to the intelligence; beyond ordinary understanding;
"mysterious symbols""the mystical style of Blake""occult lore""the secret learning of the ancients"