WARNING: The following contains spoilers for Demon Slayer: Kimetsu no Yaiba Season 2, Episode 8, "Sound Hashira Tengen Uzui," now streaming on Funimation, Hulu and Crunchyroll.
One of Demon Slayer: Kimetsu no Yaiba's longest-running mysteries was finally solved in the first episode of the Entertainment District Arc -- and by an angry drunk man of all people. Ever since his battle with Rui, Tanjiro Kamado has been hoping to find someone who can explain the Hinokami Kagura to him. This is a powerful Breathing Style that devastates demons and leaves Tanjiro unable to move after a single use, yet not even the Hashira have ever heard of it. However, Kyojuro Rengoku was able to help Tanjiro by directing him to the Rengoku family home before his death, where an answer did indeed await the young demon slayer.
Tanjiro himself learned the Hinokami Kagura from his father, who definitely did not use it to slay demons, but instead as a seemingly ritualistic dance in the snow. Since remembering the technique, Tanjiro has used it to nearly defeat Rui (who lowkey cheated) and to kill Enmu, Lower-Rank One of the Twelve Kizuki. He also used it to wound Akaza, Upper-Rank Three, although doing so cost him his blade once again. The only downside to the Hinokami Kagura is that Tanjiro can't move after performing it, making it only viable as a measure of last resort.
After Tanjiro partially heals from his wounds after the events of the Mugen Train battle, he travels to the Rengoku family home. There, he intends to deliver Kyojuro's dying words to his family, as well as search the Flame-Breathing historical records for mention of the Hinokami Kagura. Surprisingly, Kyojuro's drunken father has the answer Tanjiro has been searching for, even though he reveals it out of anger rather than helpfulness. Spotting Tanjiro's Hanafuda Earrings, Kyojuro's father accuses him of being a wielder of Sun-Breathing.
The Hanafuda Earrings, it turns out, are the symbol of Sun-Breathing, which Kyojuro's father proclaims is the original and most powerful Breathing Style. Up until this point in the series, it has been well known that the five main Breathing Styles are Water, Flame, Wind, Stone and Thunder. However, Kyojuro's father declares these to be nothing more than cheap imitations of Sun-Breathing. There's little doubt that the Hinokami Kagura and Sun-Breathing are one and the same, given that Tanjiro's own father would wear the earrings and other, similar garb while performing the dance.
It makes sense that Sun-Breathing should be the most powerful Breathing Style, given that the Sun is all demons' fatal weakness. The Style appears to have been lost to time, considering Hashira has never even heard the term Hinokami Kagura, and Tanjiro's father, perhaps the only remaining user, did not use it for demon-slaying. It's possible that this is the real reason that Muzan recognizes Tanjiro's Hanafuda Earrings and wants him dead, as he may know the truth as well that Sun-Breathers pose a significant threat to demons -- more so than users of any other Breathing Style.
At present, even after significant training, Tanjiro is rendered unable to move after using the Hinokami Kagura. If he's going to defeat Muzan and find a way to cure Nezuko, mastering the most powerful Breathing Style in existence would be the way to do it. Now that he knows the truth behind the Hinokami Kagura, it's only a matter of time before he figures out how to use it more efficiently. Once he does, Tanjiro may even surpass the Hashira themselves.