Okay, I'll tell the story of Person Of Interest as it seems some people do not know what it is (No spoilers, read ahead). John Reese (who is Jim Caviezel, just putting it out there) is a former CIA field officer and Green Beret, is living as a derelict in New York as after an incident which is unstated, causes him to be presumed dead. Then Harold Finch (Michael Emerson) comes to him and explains that after 9/11 he made a computer system which predicts future terrorist attacks. But the machine was predicting normal crimes as well. The Government were not interested, but Finch wanted to stop these crimes. In the crimes they do not know what crime it is, when it will start, or if the person they are alerted to is the victim or the person that will actually do the crime but Finch and Reese has to stop the crime either way...
So that is pretty much the story apart from the fact that they go to two police officers to help, Joss Carter and Lionel Fusco. I will stop it there as the facts are probably spoilers.