Wait—What Kind of Heights?
Contrary to what autocorrect may believe, wuthering is a real word. Our good buddies at Merriam-Webster define "wuther" as "to blow with a dull roaring sound."
Oh, well, that's cheery.
But, if you've read Wuthering Heights you'll realize that the characters take a sort of masochistically dark approach to naming things. Dogs get names like Gnasher and Skulker. Houses get names like... Wuthering Heights.
With this novel, Emily Brontë takes the whole Gothic haunted house thing several steps further than her predecessors. While the book has all of the Gothic elements made popular the century before by authors such as Ann Radcliffe and Horace Walpole—and even mocked by Jane Austen in Northanger Abbey—Wuthering Heights has a lot more psychological complexity than your average pulp Gothic job.
Throughout the story, Brontë plays on a whole set of genre conventions—Gothic, romantic, pseudo-psychological—and by naming the novel after the house, she sort of announces those influences to her readers. While the house is the main setting for most of the action, its role is so important that it almost seems like a living, breathing, ticked-off character, reflecting the bad attitude of its inhabitants.
The House on Haunted Hill
Windows and doors are a big deal in the novel, as people and ghosts are always trying to climb in or out, people are getting locked in and out, doors are slammed, keys are hidden, and so forth. Heathcliff often stands in the doorway of Wuthering Heights, controlling who crosses the threshold. At the center of the house, symbolically if not literally, is Catherine's oak-paneled bed, which provides the setting for the more uncanny and chilling events: Catherine's ghost fighting to get in against Lockwood's brutal refusal, and the death and discovery of Heathcliff's rain-soaked corpse.
To Heathcliff, whoever controls the house has the power, so even though he seeks revenge for all of his mistreatment, he does so by acquiring real estate. Being accepted into houses means a lot—Hindley never welcomes Heathcliff into Wuthering Heights, and the Lintons open their doors to Catherine (but not Heathcliff). The house has different meanings for each character—prison, punishment, social class, horror, and nostalgia.
Basically, the house is loaded with symbolic importance. It's up on the stormy hillside above Thrushcross Grange, which, by comparison, seems like a sort of Eden with its brightly lit salon and expansive garden. Lockwood notices some of the house's strange details from the very beginning—for example, the inscription over the doorway:
Before passing the threshold, I paused to admire a quantity of grotesque carving lavished over the front, and especially about the principal door, above which, among a wilderness of crumbling griffins and shameless little boys, I detected the date "1500," and the name "Hareton Earnshaw." (1.13)
This inscription serves as the house's nametag ("Hi, My Name Is Creepy, Dilapidated Mansion) and informs us that the Earnshaws have been there for a looong time (the novel is set in 1801). What Lockwood means by "shameless" we can't really know, but the implication is that the image is Gothic and a little sinister.
Oh, and bonus biographical tidbit: Emily Brontë grew up on the Yorkshire moors, so a lot of critics speculate about the influence the houses in her village of Haworth had on her description of Wuthering Heights.