"Pū-Neko" centers around a young girl named Nana, who discovers a mysterious, magical cat named Pū in her grandmother's attic. Pū possesses the ability to grant wishes, but each wish comes with unexpected and often humorous consequences. Nana, initially skeptical of Pū's powers, soon realizes the cat's abilities are real when her first wish—to become popular at school—leads to a series of chaotic events that disrupt her daily life. As Nana navigates the fallout of her wishes, she learns valuable lessons about responsibility, friendship, and the importance of careful decision-making.

The narrative unfolds episodically, with each episode focusing on a new wish and its repercussions. Nana's wishes range from trivial desires, like acing a test or winning a competition, to more profound requests, such as helping a friend in need or mending a strained relationship. However, Pū's magic often twists the outcomes in unpredictable ways, forcing Nana to confront the unintended consequences of her actions. Alongside Nana, the series features a small cast of supporting characters, including her best friend, Yūki, who provides a grounded perspective, and her rival, Rina, whose competitive nature often complicates Nana's plans.

As the story progresses, Nana begins to understand the limitations and dangers of relying on Pū's magic. The cat's enigmatic nature and cryptic remarks hint at a deeper purpose behind its presence, though its true origins remain shrouded in mystery. The series balances lighthearted humor with moments of introspection, exploring themes of self-reliance, the value of hard work, and the complexities of human relationships. By the end of the series, Nana grows significantly, learning to appreciate her own abilities and the importance of facing challenges without relying on shortcuts.