This 70-300mm VR AFS lens works on all autofocus film and digital cameras made since about 1990. It is a G-type lens with no aperture ring. It won't work on any manual focus camera.
This is the latest of many 70-300mm range zooms from Nikon. It adds Vibration Reduction (VR) to eliminate the need for a tripod, AFS focusing to allow instant manual focus override, and several hundred dollars in added expense . It's the only 70-300mm range lens that will autofocus on the D40.
It's a nice plasticy amateur lens. I don't think it's nice enough to warrant its $550 price, since you can get a fully professional 80-200mm f/2.8 AF-D for $900, and last year's model 70-300mm G for $130. Read the full review here