A focal reducer is a lens system that mounts on the rear cell of a scope in front of a flip-mirror, camera, or diagonal and eyepiece. It acts as a “wide-angle converter” and changes the focal ratio, or if you prefer, the effective focal length of a scope.
It is particularly useful when using affordable CCD cameras because they have small CCD chips and thus do not view a large area of sky. Most deep-sky objects (nebulae and galaxies) are larger than this view and you need a focal reducer to fit them on the CCD chip.
Note that a focal reducer is actually the worse thing you can do for planetary photography – planets are small and need magnification (increasing the focal ratio of a scope, for example with a barlow lens), not reduction. But if you plan to do deep-sky photography with a CCD you probably will need to get a focal reducer, especially if you don’t have (or can’t use, in the case of Meade SCTs) the Celestron Fastar system. Because they increase the effective viewing area of a scope, focal reducers have the benefit of increasing the scope’s optical (and thus photographic) speed which is beneficial for dim deep-sky objects especially if you are using 35mm film.