Even if no visible astronomical objects are present in given part of the sky, there always is some low luminosity present, due mostly to light diffusion from the atmosphere (diffusion of both incoming light from nearby sources, and of man-made Earth sources like cities). In the visible band, luminosity level is around the 25th magnitude: a very low level, but anyway well within the limits of the current generation of telescopes. The HST space telescope does not suffer from this problem.
In infrared astronomy, the problem can be much worse: due to the longer wavelengths involved, the sky and the telecope themselves are a source of light! To work around this problem, infrared telescopes often use a technique called tilting, where a mirror rapidly oscillates between the object of interest and the nearby, empty sky. The two images can be subtracted, leaving hopefully only the incoming light from the source.
In astronomical CCD technology, background is usually referred to the overall optical "noise" of the system, that is, the incoming light on the CCD sensor in absence of light sources. This background can originate from electronic noise in the CCD, from not-well-masked lights nearby the telescope, and so on. An exposure on an empty patch of the sky is also called a background, and is the sum of the system background level plus the sky's one.
A background frame is often the first exposure in an astronomical observation with a CCD: the frame will then be subtracted from the actual observation result, leaving in theory only the incoming light from the astronomical object being observed.