Here is the official synopsis
In 1971, Carolyn and Roger Perron move their family into a dilapidated Rhode Island farmhouse and soon strange things start happening around it with escalating nightmarish terror. In desperation, Carolyn contacts the noted paranormal investigators, Ed and Lorraine Warren, to examine the house. What the Warrens discover is a whole area steeped in a satanic haunting that is now targeting the Perron family wherever they go. To stop this evil, the Warrens will have to call upon all their skills and spiritual strength to defeat this spectral menace at its source that threatens to destroy everyone involved. Based on a true story.
Little backdropped on that "true story" bit. There really is a Perron family, and there really is the Warrens, a couple who "investigate" supposed ghost and demonic possession. Unlike in the movie though, their huating went one for 10 years, and didn't end after the Warrens left.
Spoilers be here!