"Dog Days" is set in the fantastical world of Flonyard, a realm inhabited by anthropomorphic animal-like beings divided into multiple nations. 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 as a "Hero" to defend her nation against the invading forces of the Galette Lion Dominion, led by Prince Brioche. The conflict between Biscotti and Galette is not a traditional war but rather a series of competitive, non-lethal battles governed by strict rules, ensuring no permanent harm comes to participants.

Shinku quickly adapts to his role as a Hero, gaining unique abilities in Flonyard, such as enhanced physical prowess and the ability to summon a magical weapon. He is joined by other summoned Heroes, including Nanami Takatsuki, a skilled swordswoman, and Rebecca Anderson, a sharpshooter. Together, they participate in various battles and tournaments, fostering camaraderie and alliances between the nations. The series emphasizes themes of friendship, teamwork, and cultural exchange, as Shinku and his companions navigate the challenges of their new environment while maintaining ties to their lives on Earth.

The narrative expands to include political intrigue, as the leaders of Flonyard's nations work to maintain peace and address underlying tensions. Characters like Leonmitchelli, the valiant knight of Biscotti, and Gaul, the stoic warrior of Galette, play pivotal roles in shaping the story's progression. Over time, the focus shifts from individual battles to larger threats, such as the emergence of ancient forces that endanger the entire realm. The series balances lighthearted moments with action-packed sequences, creating a dynamic and engaging storyline.

"Dog Days" features a diverse cast of characters, each with distinct personalities and abilities. Shinku serves as the relatable protagonist, embodying determination and kindness. Millhiore is a compassionate and resourceful leader, while Brioche provides a contrasting perspective as a rival-turned-ally. The interactions between the characters drive the narrative forward, highlighting their growth and the bonds they form. The series concludes with a resolution that reinforces the importance of unity and cooperation, leaving room for further exploration of Flonyard's world and its inhabitants.