The Great War is also known as the Three-Sided War i.e. the war between Angels, Fallen Angels, and Demons. This war had continued for generations but if we take in account with the story related to Shinmai Maou no Keiyakusha it generally relates to the war between Gods, Demons, and the Hero Clan.
According to the writer, Tetsuto Ueso's story the Gods who are tainted with malevolence are declared fallen and are exiled away to the Demon realm turning into a demon and for taking revenge against the Gods they attack on human world to destroy the Gods. So basically, the demons attack the human world and the Gods grant protection to the human world by granting special powers to the Heroes.