Nikon's Vibration Reduction system (or Image Stabilization from Canon) helps us take sharper pictures at slower shutter speeds. It's too complicated to understand or explain how it works, so just think of it as magic (see the magic here.) It's a part of lenses that are labeled with VR (Nikon) or IS (Canon) that makes photographing easier.
To understand what it does, you must first understand the problem of camera-shake. VR compensates for camera-shake allowing us to take pictures at slower shutter speeds than we would be able to unassisted. Look at what it does:
Both of these images are shown at 100% magnification, so you are seeing them pixel for pixel. Both come from much larger photographs that were each shot at 200mm with Nikon's 55-200 VR lens at a shutter speed of 1/30. The one on the left has VR turned off and the one on the right has it turned on. You can see the affects of my shaky hands on the left and the affect of VR on the right.
What does this mean?
If you remember that your options for choosing a shutter speed can be limited by camera-shake, then the benefit of VR is probably obvious. Using VR allows us to use shutter speeds that are slower without paying the price of having blurry pictures. Using the equation I gave in this post, we would expect to need a shutter speed of 1/300 to produce a sharp image at 200mm. But at 1/30 I got a decently sharp image. That's a big advantage.
