The Kingswood Brotherhood was a band of outlaws, cutthroats, bandits, and exiles who plagued the Kingswood, a forest south-east of King's Landing, approximately twenty years before the series begins. They were wiped out at the order of King Aerys II Targaryen, the Mad King. Their leader, Simon Toyne, was killed by Ser Barristan Selmy in battle, whilst Jaime Lannister, then a squire of sixteen years, killed another member of the band.
In the books
In the A Song of Ice and Fire novels, the Kingswood Brotherhood was notorious outlaw gang founded by the brothers Toyne, two outcasts whose brother, a member of the Kingsguard, had been killed by King Aegon IV Targaryen for sleeping with one of his mistresses. They ambushed and killed Prince Aemon Targaryen, the infamous Dragonknight, before disappearing into the vastness of the Kingswood. They and their descendants troubled the realm for several generations before Ser Arthur Dayne led the force of knights and soldiers - which included Ser Barristan Selmy, Lord Sumner Crakehall, and his squire Jaime Lannister who was fifteen then - who finally wiped them out.
The Kingswood Brotherhood used to kidnap nobles for ransom. They were sheltered by the smallfolk of the Kingswood, who believed that the Brotherhood was the only who protected their rights. However, Ser Arthur gained the confidence of the smallfolk by offering them better rights, thus turning the allegiance of the smallfolk to the royal forces. Without the smallfolk to shelter them, the Brotherhood members were eventually brought down. Selmy killed the gang leader Simon Toyne, while Arthur Dayne killed the Smiling Knight.
Jaime Lannister did not kill any of the Brotherhood during the fight, but saved his master Lord Crakehall from Big Belly Ben, and crossed swords with the Smiling Knight. As a reward for his bravery, Arthur Dayne knighted Jaime on the battlefield.
Other known members of the Brotherhood were Wenda the White Fawn, Fletcher Dick, Oswyn Longneck the Thrice Hanged, and Ulmer. All of the Brotherhood members are presumed dead except Ulmer, who joined the Night's Watch to avoid execution, and currently serves as a ranger
- The Kingswood Brotherhood at A Wiki of Ice and Fire (spoilers from the books)