Burning of King Olaf was a festival performed by the Bards long ago in Skyrim's history. The festival included the burning of an effigy meant to represent King Olaf One-Eye, who was sentenced to be burned for betraying Solitude. After the return of the Dragons, around 4E 201, Elisif the Fair, the Jarl of Solitude, prohibited the practice of the ritualistic burning. She felt the celebration was too gruesome, given the death of her husband, High King Torygg and the Civil War conflict between the Stormcloaks and the Imperial Legion.
If the Dragonborn of that era became a member of the Bards College, Viarmo, the headmaster, sent them to find the last remaining King Olaf's Verse, a heretical poem written by Svaknir, hoping to prove to the Jarl that the College had a legitimate claim to having the festival.
The Burning of King Olaf One-Eye is a direct parallel to Guy Fawkes Night, a similar event in the UK, where a 'traitor of the people'--Guy Fawkes-- is burned in effigy annually for their perceived betrayal.