This building serves as a home to the main protagonist, Quasimodo. By law, it serves as a refuge for those who are persecuted. Examples of this are when Esmeralda was in trouble with the law and had to stay in the cathedral or when Quasimodo saved Esmeralda and yelled, "SANCTUARY!" In the films, Quasimodo seems to have a certain attachment to the Notre Dame, even if he can interact with Parisian society, therefore making him see the cathedral as the place he belongs in.
In Real Life
Notre Dame de Paris, also known as Notre Dame Cathedral, is a Gothic, Catholic cathedral on the eastern half of the Île de la Cité ("Island of the City") in the fourth arrondissement ("Administrative District") of Paris, France. It is the cathedral of the Catholic Archdiocese of Paris: that is, it is the church that contains the cathedra (official chair) of the Archbishop of Paris.
Notre Dame de Paris appears in two occasions. The first time, Linguini passes by in his bike while going to kill Remy as instructed by Skinner. Still, he isn't capable of killing him, so he sits by the River Seine, across from the cathedral, and talks to him. The second time, Linguini and Colette pass by the cathedral while rollerskating.
Mater, Finn McMissile and Holey Shiftwell drive by the cathedral after their arrival to Paris.