The Man Upstairs is the titular antagonist of an urban legend known as "The Babysitter And The Man Upstairs".
A teenage girl is babysitting one evening. The children have been put to bed and the babysitter is in the living room watching TV. The phone rings, and she hears either silence, a man laughing, or heavy breathing. She, at first dismisses the calls as a practical joke, but she soon becomes scared when later, the caller asks her to "check the children". When she asks who he is, he hangs up. Rather than checking on the children, the teenager decides to ignore the call. The stranger calls back several times, each time angrier.
Eventually the girl calls the police, who ask her to wait for the man to call again, and they will trace the call. When he calls again, she manages to keep him talking, for a few minutes, and when the police call back, they tell her that the call is coming from a second line, inside the house, and to get out immediately, as they have already sent some officers over.
As she runs to the door, she sees a man with a bloody axe running down the stairs, and just manages to avoid his blow. She runs outside, into the waiting arms of police, who quickly kill the man.
Some versions have the children and/or babysitter killed by the man, who in some versions gets away or is simply arrested. What is summarized above is simply an idealized version of the scenario. One particular type of variation that is quite interesting is that in which the man is in plain sight rather than hiding upstairs but is initially mistaken for a statue because he is standing so still.