One of the coolest aspects of the Harry Potter series is that we get access to two – count 'em – two worlds. And all for the price of one. While Hogwarts, the School of Witchcraft and Wizardry, is the place where Harry spends most of his time in each book, at the beginning of each story we find him stuck at the Dursleys' house in Little Whinging – the Muggle world. That's right, folks, we learn through Harry that the Muggle world and the wizarding world co-exist (though the Muggle world doesn't know about the wizarding world). The wizarding world is folded into the Muggle world as magically as eggs into cake batter.
Book 1 is different from the other books in the Harry Potter series, because, at first, Harry doesn't know about the awesomeness of Hogwarts, or about the possibility of something beyond the Muggle world. Let's face it, like us when we open Harry Potter and the Sorcerer's Stone, Harry doesn't even know what Muggles are or that he's been stuck living among them.
The first several chapters of the book take place at the Dursleys' prim house on Privet Drive. The Dursleys' home may look polite and regular, with its "tidy front garden" (2.1) and its inhabitants' emphasis on behaving just like everyone else, but that doesn't make it a nice or welcoming place to live. In a way, it has just as much darkness and unhappiness as you might expect from a magical landscape. Nephew Harry is forced to live in a "cupboard under the stairs" (2.13) while the son of the house, Dudley, enjoys two bedrooms to himself. The Dursleys' house might look cheerful from the outside, but inside Harry sees only bleakness. Let's not forget that Whinging, in British English, means whining. Even the town they live in is annoying.
Along with Harry, we're introduced the magical world for the first time. And it's no wonder that Harry's so excited to get to Hogwarts, which is a school inside an actual castle. Whoa. When Harry and the other first-years first approach Hogwarts by boat, they get an intimidating and majestic sight:
Perched atop a high mountain on the other side [of a black lake], its windows sparkling in the starry sky, was a vast castle with many turrets and towers. (6.276)
The castle is massive: "[t]he entrance hall was so big you could have fit the whole of the Dursleys' house in it" (7.4). Inside, the students are welcomed into a vast enclave full of intellectual treasures and secret passageways. It takes the students forever just to figure out where to go when:
There were a hundred and forty-two staircases at Hogwarts: wide, sweeping ones, narrow, rickety ones; some that led somewhere different on a Friday; some with a vanishing step halfway up that you had to remember to jump. […] It was also very hard to remember where anything was, because it all seemed to move around a lot. (8.8)
The halls are full of classrooms, secret corridors, and trapdoors, and some parts of the castle are even forbidden. And yet, Harry feels at home here in ways he never did at the Dursleys' house, eating the best food and having the best experiences of his life. He's finally found a community.
There's only one wizarding school in England: Hogwarts. Because it has such a large student body, and because there are no nearby schools which could serve as friendly competitors in games and academics, Hogwarts is internally divided into four groups, or houses: Gryffindor, Hufflepuff, Ravenclaw, and Slytherin. The houses serve as a way of breaking the students up into academic classes within their years, a way of parceling them out into dormitories, and a way of dividing them into teams competing for points: success in academics, conduct, and Quidditch.
The houses are students' homes away from home at Hogwarts, and their companions within their houses become like family. This is particularly true for lonely people like Harry, who has no family to speak of, or Muggle-born wizards like Hermione and Dean, whose families don't really understand the other world their children are participating in.
Because our hero, Harry, and his good friends Ron and Hermione want to be Gryffindors, the Gryffindor house sometimes seems like the best one to be in. Likewise, because Malfoy and his goons are placed in Slytherin, and because all the dark wizards at Hogwarts were Slytherins, it seems like the worst house to be in. In Harry Potter and the Sorcerer's Stone, the focus is mainly on these first two houses, and Ravenclaw and Hufflepuff get kind of cheated. Later in the series, we learn more about the characters from both of those houses and why they are important.
So what differentiates these houses? According to the Sorting Hat's song, Gryffindors are "brave" and full of "daring, nerve, and chivalry" (7.33). Hufflepuffs are "just and loyal," "patient" and "unafraid of toil" (7.33). Ravenclaws are "wise" with "ready minds" and full of "wit and learning" (7.33). And Slytherins are "cunning folk [who] use any means to achieve their ends" (7.33). Put this way, it seems like Slytherins are at a clear disadvantage compared to the rest. Yet if we look at things mathematically, we realize that not everyone can be Gryffindors. The houses need to be filled equally from students in every class.