"Dog Days" is set in the fantastical world of Flonyard, a realm where anthropomorphic animals live in peace, engaging in friendly, non-lethal battles to resolve conflicts. The story begins when Shinku Izumi, a middle school student from Earth, is summoned to Flonyard by Princess Millhiore of the Biscotti Republic. Millhiore seeks Shinku's help to protect her kingdom from the invading forces of the Galette Lion Dominion. Shinku, initially bewildered by the situation, quickly adapts to his role as a hero, participating in the war games that define Flonyard's conflicts.

The battles in Flonyard are governed by strict rules, ensuring no permanent harm comes to the participants. Shinku, now transformed into a heroic warrior, fights alongside Millhiore and her loyal knights, including the skilled swordsman Leonmitchelli and the energetic mage Nanami. As the story progresses, Shinku forms strong bonds with the inhabitants of Flonyard, particularly Millhiore, whose kindness and determination inspire him. The narrative explores themes of friendship, loyalty, and the importance of peaceful conflict resolution.

In subsequent seasons, the scope of the story expands, introducing new characters and challenges. Shinku returns to Flonyard multiple times, often accompanied by his childhood friend Rebecca Anderson, who also becomes a hero in her own right. The series delves deeper into the politics and history of Flonyard, revealing the origins of its war games and the true nature of its inhabitants. Key figures such as the Galette Lion Dominion's leader, Gaul, and the mysterious warrior Couvert Eschenbach Pastillage, play significant roles in shaping the narrative.

Throughout the series, the focus remains on the camaraderie and growth of the characters as they navigate the complexities of their world. The interplay between Shinku and the Flonyard residents highlights the cultural differences and mutual respect that develop over time. The story balances lighthearted moments with more serious undertones, creating a dynamic and engaging narrative. By the conclusion, the bonds forged between the characters transcend the boundaries of their respective worlds, leaving a lasting impact on both Flonyard and Earth.