While appearing as a regular storybook in itself, the stories that can be found within King Arthur and the Knights of the Round Table have created an alternate reality, the world of Camelot, which is contained within this book. In this world, which is composed of all the tales of King Arthur and his followers, the places and characters from King Arthur and the Knights of the Round Table's stories are real and brought together, effectively making this reality a reflection of the stories themselves.
During the events of Sonic and the Black Knight, Sonic the Hedgehog was called into the world of Camelot by Merlina the Wizard in order to save this world from the corrupted King Arthur, now known as the Black Knight, and later on Merlina herself when she betrayed Sonic and tried to take King Arthur's power, the Scabbard of Excalibur, for herself.
When Sonic finally managed to restore order to the world of Camelot, the title on the front cover of King Arthur and the Knights of the Round Table was changed to "Sonic and the Black Knight", as the world of Camelot and the storybook itself recognized Sonic's participation in its stories.
Real World Reference
The book King Arthur and the Knights of the Round Table is directly taken from the real life storybooks about the Arthurian legends. To be more specific, it appears to be based on the storybook Le Morte d'Arthur (Middle French for "The death of Arthur) which was written by Sir Thomas Malory in the early 1450s and was finished in 1470, but was not published until 1485. This storybook is a compilation of nearly all the Romance tales concerning King Arthur, Guinevere, Lancelot, and the Knights of the Round Table and is regarded as the best Arthurian literature of all time.
Originally, Malory wrote Le Morte d'Arthur as eight books rather than one; The first book tells of Merlin (the wizard) arranging for Uther Pendragon's seduction and marriage to Igraine, leading to the birth of Arthur, his fosterage, his pulling out of the Sword of the Stone, and his crowning. The second deals with the establishment of the Round Table and the invasion of France and Rome. The third book mostly concerns Lancelot, who deals with Méléagant's threat to Arthur's world, and proves his devotion to Guinevere. The fourth book is about Gareth, Gawain's brother. The fifth is about Tristram and Iseult, and originates outside the world of King Arthur and his Knights, and the sixth book is about the "coming of the Grail". The seventh book is the romance between Lancelot and Guinevere, and the last and eighth book concerns the discovery of Lancelot and Guinevere's ongoing adultery, the battle between Mordred and Arthur, and Arthur's ultimate death.