Yes, there is. It's based on the idea of a spooky pizzeria with animatronics that go haywire at night. There are rumors and theories about bad things happening there, like murders or disappearances, which form the basis of the horror in the game.
There is likely some basis for the story. It could be related to the uneasiness that some people feel around animatronics in general. The thought of them moving on their own, especially in a place like a pizzeria which is supposed to be a family - friendly environment, is quite creepy. The real story might be a combination of urban legends, people's fears, and some real - life events that happened in similar settings, all mashed together to create the terrifying world of Five Nights at Freddy's.