Aside from the departments that are found in all large companies (e.g. human resources, IT, legal, payroll, &c), the major divisions of a publishing house are:
The Publisher: Within the house itself is the publisher's office, from which every book's entire creation—from acquisition to finished product—is overseen. Every other department reports to the publisher in one way or another. All major decisions are made here.
Editorial: Responsible for acquiring, editing, and effectively shepherding books through the production process, the editorial department buys books from authors via their agents, negotiates contracts, maintains relationships within the house/between the house and authors/agents, and works with production and art to organize and facilitate the creation of the final product.
Production: As you might expect, the production department is responsible for the physical creation of each book. They work closely with the editorial and art departments (as well as the publisher) to negotiate with third parties/vendors and coordinate the creation and distribution of finished books.
Marketing: In brief, marketing is responsible for any promotions that the house pays for, e.g. advertisements in various media and the creation of sales materials. They create and implement strategies to maximize a book's exposure to the marketplace, generate buzz, and identify strong markets/audiences for individual titles. They work very closely with the sales department (below).
Publicity: In contrast to the marketing department, publicity is responsible for any promotions that the house does not pay for: author appearances on TV talk shows, reviews in newspapers and magazines, and author tours/book signings/release parties. They communicate constantly with the media, writing press releases, preparing and sending press kits, maintaining databases of contacts/publications/media outlets, and mailing galleys/ARCs to critics and (increasingly) bloggers for review.
Sales: This is my department. Sales is responsible for selling books to individual accounts, be they large chains like Barnes & Noble, independent bookstores, or "special markets" that don't traditionally specialize in books (e.g. home shopping networks, home goods stores, or museums). We manage co-op (the system by which we pay retailers for premium in-store placement), maintain relationships with buyers, and mediate conversations between retailers and the publisher.
Art: Primarily responsible for the creation of book jackets, the art department works closely with the publisher, the marketing department, and the sales department to create eye-catching packaging for books. Responsibilities include securing permissions for artwork, managing any necessary freelance work, going through art morgues and stock photos for appropriate graphics, and designing and creating covers.
There are a few departments I'm leaving out for simplicity's sake, but for questions and comments, you know where to go.