Demon Slayer is about immortality and the fear of death.
I always see people arguing that Demon Slayer is a superficial work and that it only became successful because of the anime, I agree that the animation made a difference to the anime's success, but it has much more substance in the script than it appears.
One of the manga's central themes is how to deal with death.
Everything in the story revolves around this topic: the protagonist's primary motivation is to prevent his sister from dying as a demon, and along his journey, he meets others with similar motivations. Zenitsu fears death because he considers himself weak; Tomioka isolates himself after his sister and best friend sacrifice themselves for him; Shinobu harbors resentment because Douma killed her sister; Akaza became a demon after losing everything he tried to protect; and Kokushibo turned into a demon out of envy and the fear of dying from the same mark his brother bore.
Then there is Muzan, whose primary motivation is survival; everything he does in the story is aimed at preserving his own life. He seeks the ability to walk in the sunlight because he refuses to live in a world where he could die—a mindset stemming from the fact that he was born sickly and constantly facing death. He creates demons using his blood to expand his influence across Japan and—hopefully—produce a demon capable of withstanding the sun; he hunted down the family of the only swordsman who nearly killed him out of fear; and, above all, he searches for the flower that could grant immunity to sunlight.
One of the moments that best illustrates this theme occurs when Muzan invades the mansion of the Demon Slayer Corps leader. The two debate the meaning of eternity: for Muzan, eternity meant remaining unchanged and invincible—essentially, mere survival—whereas for the leader, it meant building a future of peace, being surrounded by loved ones he trusted, and being remembered by them. This highlights the contrasting philosophies regarding how to face death (it is worth noting that the leader was a dying man who had lived his entire life in ill health due to a family curse inflicted by Muzan, his own ancestor).
*Demon Slayer* concludes by upholding this anti-immortality philosophy: the heroes defeat Muzan, but at the cost of the lives of nearly the entire cast, and the protagonist himself lives only a few more years, dying young due to the sacrifices he made throughout the story.
The narrative ends with a time jump to the present day, showing the characters' descendants living in an era of peace. The work conveys the message that death and grief are overcome by seeking happiness in life, loving those around us, and striving to do our best in the world and be remembered.
It is worth noting that the author suffered a personal loss while the work was being published (some say it was her husband or her parents), which further underscores the story's message.