A millennium ago, during the Heian Era, Muzan was turned into a demon during an experimental treatment trying to cure his terminal illness, and his goal since then was to live without the fear of death and become truly eternal.
The first demon that is said to have existed was Muzan Kibutsuji. The one who turned him into a demon was a generous doctor from the Heian Period, who wanted to save Muzan from death since, at the time, he was diagnosed with a disease which would kill him before he turned twenty.
Originally a human, Muzan suffered from a terminal illness, during an experimental treatment, Muzan became the first ever demon. He is also the progenitor of most other Demons and the leader of the Twelve Kizuki. He is also the archenemy of the Kamado family and both Tanjiro Kamado and Nezuko Kamado.
In the far chapters of the Demon Slayer manga, Tanjiro is actually turned into a demon by Muzan Kibutsuji. Muzan does this to continue his demon legacy and live in this world even after being dead. He chooses Tanjiro over everyone else as he considers him the perfect one to carry on his legacy.
Curse of Kibutsuji
This curse besotted any who partake of Muzan's blood must be careful. The curse prevents Muzan's name from being spoken aloud, and any who do will meet a horrible demise. One demon, Susamaru, faced this reality when battling Tamayo.
It is revealed that Muzan's true fear of dying and immense desire to live and survive was due to him being born "dead," where his heart would constantly stop in his mother's womb and was assumed stillborn until he fought to breathe before his cremation.
Fun fact: The reason why Enmu was able to say Muzan's name out loud without dying is because they're married!
Since he didn't know anything about the Blue Spider Lily medicine, he needed others to find the plant for him by happenstance. This is the general reason why Muzan turned Nezuko into a demon. More specifically though, was the fact that Nezuko was of Kamado blood.
@IsekaiCitizen Yoriichi and the kamado family are not related but the most common and logical reason for Muzan killing Tanjiro's family is revenge.
Fans later questioned the reason for letting Nezuko live. Fans believed this could have been a strategic move from Muzan. The theory states that Muzan wanted to create a demon that developed an immunity to the sun. Upon doing so, he would consume the aforementioned demon and become invincible.
Even 400 years later, Muzan's fear of Yoriichi remained fully intact, as simply laying eyes on Tanjiro's hanafuda earrings caused him to recall their clash.
Muzan's ultimate goal is to attain an immortal body. He wanted to be able to walk in the sunlight and live forever. In order to gain this, he needed two things: the Blue Spider Lily and the body of a demon who could withstand the sun.
First hierarchy
Beelzebub, along with Lucifer and Leviathan, were the first three angels to fall.
Nezuko becoming a demon was technically planned in that she was another one of Muzan's experiments, but the type of demon she would become would surprise everyone.
However, she wasn't immune to the sunlight initially, as she got burned badly at first. So, in conclusion, her coming from a Sun Breathing user's lineage and not relying on human substance are perhaps the reasons for her immunity.
Moreover, while she was asleep, Urokodaki performed a unique hypnotism on Nezuko, making her believe that all humans are her family and she must not hurt them in any way. With her immense fondness for humanity, Nezuko broke out of Muzan's control, becoming free to do anything at her will.
The explosion, which was enhanced by spike traps, manages to injure Muzan. Before he is able to regenerate fully, Tamayo appears and uses her Blood Demon Art to keep him in place, while using a drug that can turn him into human. Using this opportunity, Gyomei Himejima appears and destroys Muzan's head.
The Thirteenth Form of the Sun Breathing Style is unique in the sense that it doesn't really have a name of its own. Rather, it's a combination of all the twelve forms present in this style, used in succession to maximize their power. This move was devised by Tanjiro solely to defeat Muzan.
There is no logical reason in relation to the plot that suggests why she has a horn. While fans might assume the horn grows on people with some relation to the sun, this wasn't the case for Tanjiro, who also turned into a demon. The only other reason that could explain the horn's existence is purely aesthetic.
Nezuko's body transforms as she breaks her bamboo muzzle, a horn grows out of the right side of her forehead and her body also becomes covered in ivy-like demon crests.
However, the trait that sets her apart from all other demons is the fact that she has the ability to conquer the sun, prompting the Demon King to call her the "chosen demon". Abnormal Demon Physiology: As the "chosen demon", Nezuko has several unique demonic traits that set her apart from all other demons.
As a human, Daki was known by the name 'Ume' instead. This was a rather peculiar choice for a name, especially since Ume was the disease that killed Daki's mother! While the death of Daki's mother was anything but tragic — given how abusive she was — his name does hint towards the manner of her demise.
History. Doma was born with beautiful and rare rainbow colored eyes. Because of this unusual trait, his parents thought that he was able to hear the voices of God and was groomed to be the religious leader of the Eternal Paradise Cult, a position that he held until his death.
Akaza appears before Muzan and reports to him that he could not find the Blue Spider Lily, instead, he took down one of the Hashira. Muzan retorts it was only one Hashira and declaring his desire is for all to be dead. Angered at his failure, Muzan takes control of Akaza's cells and causes him to bleed heavily.