Jane Eyre is both a gothic novel and a bildungsroman, or coming-of-age novel. It is a bildungsroman not only because the reader witnesses Jane's development from a child to a married adult, but also because Jane's development involves learning how to maneuver within social hierarchies to be the kind of person she wants to be.
Jane Eyre is distinct from many (not all) other bildungsromans that came before it in that it centers on a woman. It is also notable for the fact that it is narrated in the first person and is more invested in the protagonist's psychology than, for instance, a Charles Dickens novel usually is. This is because the novel seeks to investigate the proper balance of feeling and judgment in an individual (a question moral philosophers had been tossing around for several decades by this point). Circumstances and psychology are equally important to Jane's arrival at the end of her story. First person narration also allows the novel to veer into the category of the künstlerroman, a type of bildungsroman that describes the development of the artist who created it. A well-known example of a künstlerroman is James Joyce's 1916 Portrait of the Artist as a Young Man.
The gothic, which often explores social anxieties about race, gender, and wealth through horror and haunting, allows the novel to grapple with broad social implications of Jane's transformation from an orphan to the wife of a man above her station. The novel bears many hallmarks of the gothic, including haunted houses (Thornfield, the red room at Gateshead), ghostly apparitions (Mr. Reed, Bertha's disembodied laughs), and ill-gotten wealth that must be somehow dispensed with (Mr. Rochester's money). Thornfield is haunted because, as an estate, it consolidates the wealth Mr. Rochester got through business in the British colonies. Bertha, as a haunting presence, represents not only herself but also all the people Mr. Rochester and the practice of colonization have harmed.
By relying on gothic tropes, Brontë makes Jane's development arc a solution to national anxieties about imperialism. Estates that are entangled with colonial wealth are doomed to burn down like Thornfield, the novel seems to imply. Their corrupt history is too destructive. Instead of becoming a self-made individual by investing outside England's borders, as Mr. Rochester does with his first marriage, the novel suggests that people might make their modest fortunes by marrying fellow English people for love and security (not outsized wealth).