A story needs to be imagined by someone. This person who does this is the most important part of any role play game.
Their name varies depending on the game. In a tabletop game you would usually find they call themselves either a Games Master or a Dungeon Master. The same role in a Live Action Role Play (LARP) , such as Elements, would usually go by Head Referee.
My last GM, David Chapman, talks to me about his experiences with tabletop role play games and how they helped him get through day-to-day life. He volunteers as a Games Master at LvlUp, where you can sign up to play his home-made systems.