The phrase "mysterious man" refers to a man who is difficult to understand or figure out. He may have an air of secrecy around him, making it hard to know what he is thinking or what he is up to. Full definition
When she arrives, she meets a dark and mysterious man at the bar. (dailyfreebooks.com)
It's about a plot to assassinate someone, but she's not sure whom (a plot hole a mile wide and then some), and so, even though she's being stalked by mysterious men driving big cars with malicious intent, she doesn't tell anyone right away. (killermoviereviews.com)
Meanwhile, a pair of mysterious men with mysterious motives uncrates their own underwater craft. (parentpreviews.com)