Proper Japanese Title: 鬼滅の刃
Originally serialized in Weekly Shonen Jump, Kimetsu no Yaiba follows the struggles of Tanjiro Kamado as he is forced into a life of killing demons and trying to save the last surviving member of his family (Nezuko). Set in the Taishō period of Japan (1912-1926), at the start of the story he is the eldest child (13 years old) in a family of six that lives up in the mountains and has lost its father.
Happy to put his siblings before himself, he goes down the mountain in the winter to the nearest town to sell the coal he carries on his back and buy some food for his family. However, on the way back, he is urged by a concerned man to stay the night because it would be unsafe to climb the mountain. However, when he does arrive back home in the morning, he finds his entirely family has been brutally murdered and the only one with any pulse at all is the next-oldest child, his sister Nezuko.
When she awakes, and through the intervention of a demon hunter (Tomioka), Tanjiro learns that his family was killed by a demon and now his sister has become one. Though he warns that most people will want to kill Nezuko, he does recommend him to a man (Sakonji) who trains him for two years to become a swordsman capable of killing demons while also teaching Nezuko to always help humans.
Thus, after passing a final exam, Tanjiro is able to join a demon-killing organization where he is regularly sent on missions to deal with new threats (primarily demons that are in the process of terrorizing or killing civilians or other members of the organization).
Besides Nezuko (who he carries on his back in a specially-made wooden box) being a demon, Tanjiro's endless empathy for anyone he comes across (including the demons he kills), makes him a unique figure in the world of demons and can put him at odds with his own allies (including many of the Pillars, who are the elites of the organization).
However, his personality of wishing to help others has also gathered around him some misfit allies including a demon hunter who is afraid of demons (Zenitsu) and one who doesn't care who he fights as long as he proves he's the strongest (Inosuke).
Currently, Tanjiro's ultimate goal is to find a cure for his sister, but to do that he has to get the blood of the first demon, Muzan, who killed his family or at least the blood of his own closest servants (the Twelve Demon Moons) with whom he often shares his blood to grant them increased power.
As these elite demons are all hundreds of years old at least and have killed Pillars from past eras, Tanjiro must also constantly work to become stronger in the hopes of even reaching their level, though he has already attracted enough attention that demons are also sent personally to kill him by Muzan himself.