To arouse the curiosity or interest of by unusual, new, or otherwise fascinating or compelling qualities; appeal strongly to; captivate. (Dictionary.com)
To achieve or earn by appealing to another’s curiosity, fancy, or interest: (Dictionary.com)
To draw or capture: (Dictionary.com)
To interest someone a lot, especially by being strange, unusual, or mysterious: (Cambridge Dictionary)
Arouse the curiosity or interest of; fascinate. (Oxford Dictionaries)
Make secret plans to do something illicit or detrimental to someone. (Oxford Dictionaries)
Intrigue is the making of secret plans to harm or deceive people. (Collins Dictionary)
If something, especially something strange, intrigues you, it interests you and you want to know more about it. (Collins Dictionary)
The twenty five most intriguing people of the year. (2012)
Forty intriguing words to introduce to your vocabulary.
The word intrigue starts with an I and there can be intriguing person, books, quotes, movies etc. They interest you to learn more about them because they are mysterious, or strange.