Through his mother's family, he is the last descendant of the wizard Salazar Slytherin, one of the four founders of Hogwarts School of Witchcraft and Wizardry.
The Peverells, Gaunts, Blacks, Malfoys, Potters, Weasleys, Prewetts, and other families are all linked to one another through bloodlines and intermarriage. The only known direct descendants from Salazar Slytherin were the Gaunts, who for the most part shared their ancestor's beliefs in the purity of wizard blood.
Family members
Salazar was the father of Severus Snape, the father-in-law of Snowdrop Evans and Tom Riddle, and the second maternal grandfather of Violet and Solana Peverell-Prince-Gaunt. Salazar was abusive, mentally, physically, and emotionally, towards his son while Norabelle was neglectful, cold, and callous.
Voldemort was Salazar's heir, and as far as it is explained, he is taking up the mission in the way he believes Salazar had intended, with the Chamber and the Basilisk.
While it's true that Voldemort is a descendant of Salazar Slytherin, he is the “Heir of Slytherin” because he is a parselmouth and he figures out he needs to communicate with the basilisk to open the Chamber of Secrets. Tom Riddle, Jr simply appropriates the title “Heir of Slytherin” for himself.
Harry is the Heir of Gryffindor (though his powers have been bound by his father when he was a baby), Neville is the Heir of Hufflepuff, Meghan (OFC, daughter of Sirius) is the Heir of Ravenclaw. Harry/Ginny, Ron/Hermione, Remus/Tonks.
Her real parents were Daneel and Dean Novak, Pureblooded wizards. Turns out Daneel was Tom Riddles younger sister, Daneel Riddle. Of course, the Riddles were related to Salzar Slytherin himself, and this made Hermione the living heir of Slytherin. The problem with being a female Slytherin heir, is that they're cursed.
Neither of them is Slytherin's heir. Although, as Dumbledore says, Harry's ability to speak Parseltongue is a skill accidentally transferred by Slytherin's actual heir, Voldemort, when he tried to kill Harry as a baby. So perhaps this is one myth with a bit of truth to it.
The Heir of Hufflepuff was none other than Cedric Diggory, who was well on his way to fulfilling the prophecy of the Heir of Hufflepuff when he was tragically murdered by Peter Pettigrew.
Harry and Neville are both heirs of Gryffindor, as are all the other wizards who did the same throughout time.
Harry himself is a half-blood, since his pure-blood father, James, married a Muggle-born witch named Lily, and his maternal grandparents were Muggles.
But when they went to Hogwarts, everything changed. The pair were parted when the Sorting Hat placed Severus in Slytherin and Lily in Gryffindor, and while Lily thrived in her new, magical life, Snape was essentially placed in close quarters with the likes of Lucius Malfoy, Avery and Mulciber.
Why didn't the Potters make the Sacred Twenty-Eight? Potter is a common Muggle surname. Harry's family didn't make the list, according to J.K. Rowling, because 'the anonymous compiler of that supposedly definitive list of pure-bloods suspected that they had sprung from what he considered to be tainted blood'.
Moaning Myrtle
Born in the late 1920s to Muggle parents, Myrtle Warren started her Hogwarts life in the early 1940s, where she was sorted into Ravenclaw.
He was a descendant of Salazar Slytherin, and the knowledge caused him to despise his parents for severing his connection to his heritage. As the mystery of his origins was revealed, Tom decided to separate himself from his father's last name and go by Lord Voldemort.
Unfortunately, that man was the Bloody Baron, who was head over heels with Helena, and stabbed her in a rage when she refused to come home. After Helena was tragically killed, legend tells us that Rowena Ravenclaw died of a broken heart.
Who were the heirs of each of the four founders of Hogwarts? Ravenclaw heir is the Grey Lady; aka Helena Ravenclaw. We do not know if she has any other children or if Helena had any children. So we don't know if there are any Ravenclaw heirs alive at the time of Harry's hogwarts days.
Actually Albus Dumbledore was a Gryffindor.
After Voldemort's death in 1998, Delphi became Salazar Slytherin's last known heir.
Harry Potter came very close to being sorted into Slytherin before he persuaded the Hat to sort him into Gryffindor. Yet the spectre of Slytherin haunted him for some time afterwards, becoming particularly potent in Harry Potter and the Chamber of Secrets, when he was rumoured to be the heir of Slytherin.
Known Parselmouths
Ginny Weasley was able to speak Parseltongue while she was possessed by Tom Riddle's Diary, which enabled her to open the Chamber of Secrets.
He is proud
Pride is a key Slytherin trait, and arguably Albus has it in cauldrons. Sometimes this is to his advantage, like when he takes pride in having a friend like Scorpius Malfoy, who is funny and clever and kind, no matter what the rumours say about him and his parentage.
Hermione Malfoy (née Granger) is the daughter of Mr Granger and Mrs Granger, wife of Draco Malfoy, Daughter-in-law of Lucius Malfoy and Narcissa Malfoy (née Black), Mother of Hyperion, Hyperion II, Scorpius, sister-in-law of Miss Malfoy and friend of Harry Potter.
Albus ended up in Slytherin because he couldn't stop thinking about ending up in Slytherin, and so the Sorting Hat couldn't grasp anything other than his thoughts about being in Slytherin.