1) Using an office metaphor, a desktop is a computer display area that represents the kinds of objects one might find on a real desktop: documents, phonebook, telephone, reference sources, writing (and possibly drawing) tools, project folders. A desktop can be contained in a window that is part of the total display area or can be "full-screen" (the total display area). Conceivably, you can have multiple desktops (for different projects or work environments you may have) and switch among them.
In its Windows product, Microsoft provides what they call an Active Desktop. It includes representations of and access to desktop objects and also dynamic Web content as well, including integrated links to Web sites and information areas that are generated as the result of sites pushing requested information updates to the user.
2) Desktop is also an abbreviated form of desktop computer, a personal computer that fits on top of a desk.