Crop factor
Full frame sensor a CCD or CMOS sensor the same size as a 35mm film exposure (i.e. 24 x 36 mm).
Lenses designed for full frame sensor sizes can be used on cameras with smaller sensors. The effect is of having a lens with a longer, 35mm-equivalent focal length (e.g. a 28mm lens on a Canon 20D is like a 45mm lens on a 35mm camera).
Lenses designed specifically for smaller sensor sizes usually won't work on larger sensor sizes as they do not provide enough coverage. Automatic control of CPU enabled lenses is also an issue when using older 35mm cameras.
Canon
Canon's digital SLRs use 3 different sized sensors:
Nikon
Nikon's consumer and prosumer digital SLRs - D40-D200 - have a 1.5x crop factor. Lenses designed for this sensor size have the DX description; these do not provide enough coverage for full frame sensors or 35mm cameras.