The Festival of the Mother is a religious holiday dedicated to the Mother, an aspect of the seven-faced deity of the Faith of the Seven. Presumably, it is celebrated every year throughout King's Landing and the realm.
King Tommen I schedules the trials of the Queen Mother Cersei Lannister and Ser Loras Tyrell to be held at the Great Sept of Baelor during the Festival of the Mother. Additionally, King Tommen declares trial by combat to be forbidden throughout the realm after conferring with the High Sparrow, who holds considerable influence over the young king.
Shortly after the trial of Loras Tyrell during the festival, the Great Sept of Baelor is destroyed with wildfire in a plot orchestrated by Cersei Lannister to avoid her trial. The plot kills nearly the entirety of the Faith Militant and the Sparrows, including the High Sparrow himself, as well as a large amount of the nobility and the smallfolk of the capital.