The Egghead Arc includes the following characters: Straw Hat Pirates (Monkey D. Luffy, Roronoa Zoro, Nami, Usopp, Sanji, Tony Tony Chopper, Nico Robin, Franky, Brook, and Jinbe), Dr. Vegapunk and his six satellites, Jewelry Bonney, Bartholomew Kuma, the CP0 agents, the members of the World Government—particularly Saint Figarland Garling—and the Five Elders.
The arc takes place on the futuristic island of Egghead, which serves as a base of operations for Dr. Vegapunk. By far the most important reason this arc is necessary is the sudden visit of the Straw Hats to Egghead and their consequent involvement in the convoluted intrigue surrounding politics and science, both related to the studies Dr. Vegapunk conducts.
After the Straw Hats' arrival on the technologically advanced island of Egghead, the development of an Egghead Arc kicks in. There, they meet Dr. Vegapunk, a brilliant mind who had been working on research very important to the World Government. Pretty fast into the arc, though, things get interesting as it is revealed that he has been working on forbidden themes like the Void Century, and then the World Government sends CP0 to kill him. Things are further complicated by Jewelry Bonney, who is in search of information about her father, Bartholomew Kuma.
The Straw Hats get entangled in a huge, complicated tapestry of scientific advancements, political intrigue, and historic revelations as they press deeper into the depths of Egghead. This arc introduces the notion of the Six Satellites, based on aspects of Vegapunk's personality in different bodies, which further adds to the depth of interaction the characters share. As such, the events described are, therefore, played out with advanced technology at the forefront—the Seraphim, artificial human replicas based on Warlords of the Sea.
The arc delves into Bartholomew Kuma's past and the tragic events, including his connections with Bonney and the Revolutionary Army, which led him to be in his current state. This provides an emotional depth to the arc and relates to broader themes of sacrifice and the nature of free will in the One Piece world.
As the situation on Egghead becomes increasingly unstable, the arc escalates with the addition of direct antagonists in the form of the Five Elders, significantly deteriorating things between the Straw Hats and the World Government. With their presence, coupled with that of CP0, things go up a notch and finally provide clues regarding the highest level of power in the world of One Piece.
It also trudges into other events unfolding elsewhere, like the kidnapping of Pudding and Koby by the Blackbeard Pirates and Garp's rescue mission, hence expanding into global conflicts in the ongoing fights. In general, these subplots fuse the events of the Egghead Arc into the whole storyline of One Piece while setting up subsequent plot lines.
Arc themes include scientific morals, what it means to be human, and the perils of researching forbidden knowledge. On a larger scale, world-building in One Piece expands in the Egghead Arc considerably with its glimpse into advanced technology, the inner mechanisms of the World Government, and the secrets of the Void Century.