A man was in Florida, in 1989, when his friend was killed in Brooklyn (one of New York City's 'boroughs' or 'areas').
However, he was arrested by the police and charged with (accused of) the murder. He was put on trial (to be put on trial means to go into a courtroom before a judge or jury to determine whether a person is guilty or not guilty) and he was found guilty. (I do not know whether a judge or a jury found him guilty. A jury is made up of 12 regular citizens.) After 25 years, he is being released. He was falsely thrown in jail when he was 27 and he is now 51.
I guess the 'hero' of the story is Ken Thompson. He is the new head of the District Attorney's Office of Brooklyn. So he is in charge of all the lawyers who 'prosecute' people who have been accused of crimes. To prosecute someone is to take the person to trial to try to find the person guilty. A 'prosecutor' or DA (District Attorney) argues that a person is guilty while the 'defense attorney' argues that his client is innocent.
Ken Thompson has learned that many innocent people were thrown in jail in Brooklyn in the past, and he is trying to get all of these innocent people released.