Aniplex of America describes the story:
It is the Taisho Period in Japan. Tanjiro, a sympathetic kid who sells charcoal professionally, discovers his family butchered by an evil spirit. To exacerbate the situation, his more youthful sister Nezuko, the sole survivor, has been changed into an evil presence herself.
In spite of the fact that crushed by this horrid reality, Tanjiro takes steps to turn into a “demon slayer” so he can transform his sister over into a human, and slaughter the evil presence that slaughtered his family.
Akira Matsushima is the character originator, with Miyuki Sato, Yōko Kajiyama, and Mika Kikuchi filling in as sub-character planners. Yuki Kajiura (Sword Art Online, Fate/Zero, Madoka Magica) and Gō Shiina are making the music. Hikaru Kondo is creating the arrangement.