The swordsmen of Demon Slayer: Kimetsu no Yaiba utilize various breathing techniques to fight against the threat of demons. While each form is unique in its own right, Sun Breathing is known as the original style. Let's take a look at its history within the series.
Tanjiro's fight against Rui provides the first glimpse at his Hinokami Kagura Dance, which, aside from being one of the most beautifully animated scenes in the anime, is a significant moment. At first, it appears to be a ritual passed down through generations of Tanjiro's charcoal-merchant family as a dance and offering to Hinokami, the Fire God, that he learned from his father. However, the dying Kyojuro Rengoku, the Flame Hashira, tells Tanjiro that books at his family's home may contain information on the Hinokami Kagura.
Tanjiro's Inherited Memories Explained Sun Breathing
At Rengoku's house, Tanjiro meets the Flame Hashira's younger brother, Senjuro, and father, Shinjuro. This meeting isn't well-received by Shinjuro who, after seeing Tanjiro's hanafuda earrings, assumes he practices the art of Sun Breathing, but it's a term Tanjiro has never heard. The aggressive and grief-stricken former Flame Hashira tells Tanjiro that all other breathing forms are nothing more than imitations of the original Sun Breathing. Under the impression that Tanjiro is there with a superiority complex as a Breath of Sun user, Shinjuro wants nothing to do with the young Demon Slayer.
Still hoping to find some answers, Tanjiro and Senjuro find the book that Rengoku mentioned, but it has been too severely damaged to read. Though Tanjiro doesn't learn much new information, Senjuro later sends him a letter after finding that the Hinokami Kagura has 13 forms. Tanjiro eventually confirms this for himself and gains a better understanding of Sun Breathing following a series of strange dreams -- called inherited memories -- from his ancestor Sumiyoshi.
In these memories, Tanjiro experiences events from the life of Sumiyoshi, a distant ancestor of his, who spoke with Yoriichi Tsugikuni. Yoriichi was both the creator of Sun Breathing and a legendary swordsman from the Sengoku period. As a Demon Slayer, he is renowned as the strongest in the organization's history, pairing his breathing technique with his Demon Slayer Mark and ability to see the Transparent World. With the combination of those skills and his inherent talent, Yoriichi almost single-handedly defeats Muzan during their fight.
Yoriichi is deeply pained by his inability to kill Muzan and views himself as a failure for allowing the demon to continue hurting people. In the memories, Tanjiro observes Yoriichi performing 12 of the Sun Breathing formations, which help him perfect his usage of the technique. It is thanks to Sumiyoshi that the movements are passed down through the generations and eventually become known as the Hinokami Kagura. Since Yoriichi didn't have any heirs, he leaves Sumiyoshi with his signature hanafuda earrings, that are ultimately inherited by Tanjiro.
Sun Breathing Allows Tanjiro to String Attacks Together
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In the time since Yoriichi's death, Muzan and the Upper Rank 1 demon, Kokushibo, who is also Yoriichi's twin brother, killed anyone who knew Sun Breathing. While there are still descendants of Breath of Sun users, like Muichiro Tokito, the Mist Hashira, it's Tanjiro's family who helped keep the original style alive. As the final battle against Muzan rages on, Tanjiro realizes the connection between his family's dance and Sun Breathing.
Yoriichi's spirit-like movements as he performed the 12 forms reminded Tanjiro of something his father said, "If you learn how to breathe properly, Tanjiro, you'll be able to dance forever." He realizes that the 12 formations can be connected by the "Dance" and "Flame Dance" forms, thus completing a ring that allows him to string attacks together continually. The successful combination of all 12 results in the 13th form, which proves instrumental in the decisive battle.