What it means by AF-S DX VR Zoom-Nikkor 55-200mm f/4-5.6G IF-ED?

Camera lens

It means its a mid to telephoto zoom lens, with a focus motor in the lens body (AF-S), made especially for cropped sensor cameras (DX) and it has image stabilisation built in (VR). The 55-200mm is the focal length range it covers. F4-f5.6 means the maximum aperture the lens is capable of between its focal length ranges (f4 at 55mm, f5.6 at 200mm) and it is a G lens which means it has no aperture ring on the lens (aperture will be controlled by the camera body). IF-ED refers to the lens coatings.

AF-S is an autofocus lens that has its own autofocus motor
DX is cropped frame
VR is vibration reduction
Zoom means it can change focal length
Nikkor is Nikon's lens system
55-200mm is the focal length range
f/4 is the max aperture at 55mm
f/5.6 is the max aperture at 200mm
G is Nikon's designation of no dedicated aperture ring and AF-S
IF is internal focusing (meaning the lens will not extend or retract when focusing)
ED is Nikon's extra low dispersion glass element

It means it's a standard to telephoto zoom lens.

Anything below 35mm is considered to be wide, and above 85 to be telephoto. Between is standard. The more mm there are, the longer the lens goes.

f/4-5.6 are just aperture openings, the lower the number the bigger the aperture can be. G, IF-ED are features, AF-S too and DX is a type of lens.

Here's a Lens Buying Guide - http://www.the-dslr-photographer.com/2009/11/buying-a-lens/