"We... we are alone, aren't we?"
'Yes, of course. Well, Wormtail's here, but we're not counting vermin, are we?"
-- Narcissa Malfoy and Severus Snape (HBP2)
"...the Dark Lord is pleased that I never deserted my post: I had sixteen years of information on Dumbledore to give him when he returned, a
rather more useful welcome-back present than endless reminiscences of how unpleasant Azkaban is. . . ."
-- Severus Snape to Bellatrix Lestrange (HBP2)
This brick row house is almost certainly where Severus Snape grew up, and then lived alone for most of his adult life. Narcissa Malfoy and Bellatrix Lestrange sought him out here in 1996, when he made an Unbreakable Vow to Narcissa that he would kill Dumbledore if Draco failed to do so. Wormtail was living there to help Snape out at the time as well. The house itself is quite small, with a tiny sitting room whose walls were completely covered with bookshelves (even the door is hidden behind a bookshelf) and which “had the feeling of a dark, padded cell” (HBP2). The furniture is old and threadbare and the room is lit by a “candle-filled lamp” instead of Muggle electricity. Snape ordered Wormtail to serve some elf-made wine, which led to an argument, then Pettigrew being sent to his room.
Snape has another connection to wine, which is perhaps fitting as a Potions Master. He used nettle wine as one of the choices in the Potions Riddle which was set up as a defense against Voldemort getting the Philosopher's Stone. Since it was a logic puzzle, he probably thought most wizards couldn't pass it, yet Quirrel got through with the help of Voldemort, and Harry got through with the help of Hermione (PS16).
Peter Pettigrew, also known as Wormtail, was staying with Snape at the time to "assist" him with some unknown task. His purpose there may also have been to spy for Voldemort, which is why he avoided Snape's eyes in case he cast the Legilimens spell to view his thoughts. Snape treated Peter like a common servant, ordering him to serve the elf-made wine, then sending him to his room. Wormtail was not only part of the Marauders, the group of bullies who attacked Snape as a boy, he was also the traitor who sold out the Potters leading to the death of Lily, then helped the Dark Lord rise again in the graveyard. Snape probably enjoyed getting some long-smoldering revenge by ordering Wormtail around.
A major unknown in the canon is what happened to Snape's parents, the original owners of the house in Spinner's End. Are they dead, or did he hide them somewhere during the first war with Voldemort? Snape's father was a domestic abuser, so some fans have suggested maybe he went to jail, which would parallel Dumbledore's father going to Muggle prison, and Draco's father Lucius and Harry's godfather Sirius going to Azkaban. But what happened to Eileen Prince? One popular fan theory is that she became "Irma Pince," the Librarian at Hogwarts, whose name is an anagram for "I'm a Prince." Irma's appearance and manner certainly matched Snape's with a large nose and vulture-like way of sneaking up on people (CS10). It would also be ironic, since she is mentioned in the introduction to Quidditch Through the Ages (QA/f), which Snape took away from Harry in year one, telling him no library books were allowed outside the school, sounding just like Irma (PS11). The question is whether she might have been obliviated to forget Snape was her son, or did they still have a mother-son relationship? The last time she was seen in the story was at Dumbledore's funeral, although under a thick black veil being escorted by Argus Filch. It's possible that Snape was actually masquerading as Irma in that scene so he could attend the funeral, but that is just speculation. It wouldn't be the first time Snape appeared in the story wearing a dress - he was also Neville's boggart dressed as his Gran and carrying a red handbag.
In researching possible locations for Spinner's End for his book In Search of Harry Potter, Steve VanderArk took this photo of an odd house at the end of a cobblestone street with a chimney in the distance, just up from the river, in the town of New Mills in the north of England. One can easily imagine this almost-windowless house being that of the Snape family.