Jaime Lannister and Meryn Trant plan security for the royal wedding in the White Sword Tower. King Joffrey Baratheon reads about the great deeds of Arthur Dayne and Duncan the Tall in The Book of Brothers. He finds Jaime's entry to be very short and sarcastically says Jaime's great deeds are not in the book.
While in the Tower, Brienne of Tarth reads Jaime's entry in The Book of Brothers. Shortly after, Jaime gives Brienne his Valyrian steel sword, a new set of armor, and the mission to locate and protect Sansa Stark.
Having become Lord Commander of the Kingsguard following the Battle of King's Landing and the deaths of all Cersei Lannister's Queensguard, Ser Brienne looks over The Book of Brothers in the White Sword Tower, tearfully recording the deeds of Jaime in the War of the Five Kings and Daenerys Targaryen's war for Westeros.
In the books
In the A Song of Ice and Fire novels, the White Sword Tower is a slender, four story structure built into an angle of the Red Keep's wall overlooking the bay. A circular white room, known as the Round Room, has whitewashed stone walls hung with white woolen tapestries, and forms the first floor. A large white table - weirwood carved in the shape of a shield - with seven chairs provides a meeting space for the order. The undercroft holds arms and armor, the second and third floors the small spare sleeping cells of the six brothers of the Kingsguard, and the topmost floor is given over to the Lord Commander's apartments. His rooms are spare as well, but spacious, and they stand above the outer walls. The Tower also houses The Book of the Brothers, also known as the White Book, in which the deeds of each member of the Kingsguard is recorded.