All colours in our visual range are made up of a combination of the three primary colours, red, blue, and green. In the bluescreen process, an actor or object is filmed against an evenly lit (i.e. entirely one colour) blue screen. In the compositing process, the blue element (i.e. the background screen) is removed via a colour separation process. The screen is blue in colour because blue is the smallest competent in the colour of human skin (i.e. skin colour has more red and green elements), so that when the blue colour is removed, it does not affect the appearance of the skin. This of course also means that the actor cannot wear certain blue clothing or the object cannot have blue parts.
With digital technology having almost completely replaced the traditional compositing processes, the colour of the background screen is becoming less important as greater accuracy in colour separation can be achieved with computers. In the television series Lois & Clarke: The New Adventures of Superman, the Man of Steel was filmed against a green screen for the flying shots to prevent his blue tights from disappearing into the composited background.
More information about bluescreen can be found in various books on special effects techniques, at the Blue Screen/Chroma Key Page, Bluescreen.com and of course in the trusty old American Cinematographer Manual from the ASC.