Before I answer your question, I'd like to start with some brief recap! If you don't need a recap, jump down to "BOOK 24 PURPOSE" at the end
Brief Story Overview:The Odyssey by Homer is one of the most praised pieces of writing within English Literature due to its strong foundation of self-discovery and development of character through moral lessons. It's an epic poem which follows the journey of Odysseus, King of Ithaca, who leaves his home to fight in the Trojan war. After a 10 year battle, Odysseus and his crew win against Troy. However, unbeknownst to him, he spent another 10 years JUST TRYING TO GET HOME! Between run-ins with Greek Gods and Goddesses, such as forced infidelity, losing crew members and battle with Greek God/Goddesses, his trip back to his wife, Penelope, and only son, Telemachus, was filled with emotional turmoil, bewilderment and true test of character. During Odysseus’s absence, Penelope was constantly tormented by suitors who aspire to overthrow Odysseus’s position as King and force Penelope to be their new wife.
Book 23 Recap:
Understanding Odysseus has been away from home for some time, he finally returns in book 23. When he returns, he kills all of Penelope’s suitors, and Penelope is in shock that he has finally returned (Remember, it’s been 10 years).
Book 24 Recap:
After Odysseus kills Penelope’s suitors, The messenger God, Hermes, has now led all souls of the suitors to Hades, AKA the Underworld, AKA, “Land of the Dead.” Meanwhile, in the land of Ithaca, Odysseus, meets again with his father and former King, Laertes, who doesn’t recognize his son due to premature aging from grief/pain due to Odysseus’s 10 year disappearance. After proving his identity through his known scars, Odysseus shares lunch with his Father. Suddenly, a goddess flies through the air to share news that parents of the suitors, who Odysseus just killed, were planning revenge against Odysseus.The parent create an army and head to Laertes’s home with Odysseus, however, Odysseus’s mentor (she serves as a mythical guardian angel/warrior for Odysseus) stops violence from persisting by forcing them to forget their planned massacre and children and recognize Odysseus as King once again.
Book 24 Purpose: The answer to "Is Book 24 needed?"
Overall, although many argue Book 24 was unnecessary, it actually proved clear purpose for closing story plot gaps, redefining character motivations and reestablishing an overarching theme. To give context, story plot gaps were closed from Book 11, which, shows Odysseus in Hades where he find out out from his mother that his father was suffering greatly from his disappearance. To avoid story plot gaps, Book 24 works effectively to to show Odysseus's father's mental state upon his son's return and shows how they are finally at peace. However, despite the peace Odysseus and his father now feel, there's still a final problem; the suitors' loved ones reaction to Odysseus's killing of their family members. Considering this was a new problem as a reaction from Book 23, the Greek Goddess's sudden arrival and ability to stop any madness before it occurs further reestablishes the story's reoccurring theme, the power of the Gods. We see throughout the epic poem how much power and influence they hold throughout the story, ultimately showing, that the livelihood, fate and end of humans is still within their control and mortals, humans, must always praise and keep their honor in mind.