"Illicit" means illegal. So if you do something "illicitly", you do it in a way that's against the law.

If you saw it in a book, you should provide the context to get an exact answer. Some examples: Marijuana’s legal here now, but when I was young some of my classmates enjoyed it illicitly. (They used it illegally. ‘Enjoy’ suggests that they perceived it as a positive) ‘Illicit’ can also be figurative. My doctor doesn’t want me to eat junk food, but since it’s my birthday I figure I’m entitled to enjoy it illicitly. (Against the rules given by the doctor)

Try "guilty pleasure"