- "Maegor...mounted the black dragon, Balerion, and burned down the sept in King's Landing while the Faith Militant were inside at morning prayers. The screams of the burning and dying men were said to echo throughout the city. "
- ―High Sparrow
The Burning of the Sept of Remembrance was a massacre during the Faith Militant uprising.
When the Faith Militant rose in revolt against House Targaryen, they overwhelmed the new capital city King's Landing, causing the weak King Aenys Targaryen to flee to Dragonstone - where he soon died from the stress. Aenys's half-brother Maegor Targaryen then usurped the crown and returned to King's Landing, where he challenged the Faith Militant's champions to a trial of seven to prove his right to rule.
After emerging victorious, Maegor rode the great black dragon Balerion across the city to the Sept of Remembrance, headquarters of the Faith Militant's local chapter, where all of its members were gathered for morning prayers. Balerion's flames burned down the entire sept and immolated everyone inside - in single stroke, wiping out the Faith Militant's presence in the capital city and restoring control to House Targaryen.
In the books
Maegor was actually fell into a coma from the wounds he took in his trial of seven against the Faith Militant's champions - though of the fourteen men who walked onto the field he was the only one left alive.
He remained unconscious for about a month in the Red Keep, until his mother the Dowager Queen Visenya Targaryen sent for Maegor's polygamous third wife, Tyanna of Pentos, from across the Narrow Sea. Rumored to be a sorceress and alchemist skilled with poisons but also medicine, Tyanna managed to treat Maegor, who woke with the sun the next day.
When Maegor publicly appeared again for the first time on the walls of the Red Keep, the crowds cheered and celebrated - but their cheers soon died when he mounted the dragon Balerion, and promptly flew from Aegon's Hill to Rhaenys's Hill on the other side of the city. The Sept of Remembrance was located atop the hill, which was being used as the local headquarters of the Faith Militant's King's Landing chapter. Specifically it was the headquarters of the Warrior's Sons, the upper order of the Faith Militant, composed of well-armed and trained former knights and younger noble sons (the TV series condensed this so no mention is made of the Faith Militant actually being composed to two internal orders, the lower one being the Poor Fellows).
Maegor burned down the sept while the Faith Militant were all gathered inside for morning prayers, at a stroke destroying the entire King's Landing chapter of the Warrior's Sons and totally retaking control of the city, which they had seized from his weak brother Aenys. Maegor also deployed archers around the Sept of Remembrance in advance, to pick off any men who tried to escape, ensuring there would be no survivors or prisoners taken. According to semi-canon sources, 700 Warrior's Sons burned to death in the conflagration.
A pall of smoke hung over King's Landing for days afterward, but it was only the first act of a war which would last throughout Maegor's six-year reign. His first act upon sitting the Iron Throne again was to send out messages commanding all loyal lords in the Seven Kingdoms to raise their armies to destroy the Faith Militant - and in response, the High Septon sent messages out from Oldtown across Westeros commanding the Faith Militant to raise its armies against the Targaryens, as well as for all pious lords to turn against Maegor.
The "Sept of Remembrance" was so-named in honor of Aenys's mother Rhaenys Targaryen, who had died thirty years before in the First Dornish War - as opposed to Maegor's still-living mother Visenya, who always resented that Rhaenys's son Aenys was put ahead of her son in line of succession. Maegor's destruction of the sept was thus also something of a slight against the rival branch of House Targaryen (though Aenys was dead, Maegor usurped the throne ahead of Aenys's five children; three sons and two daughters). A few years later, as if to hammer home his dominance over the Faith Militant, instead of having the sept rebuilt Maegor ordered that a massive "stable for dragons" should be built over its ruins: the Dragonpit.