AF-S 18-55mm VR Kit Lens. What is this lens specification mean?

I know Nikon D5100 has no built in auto focus motor. If I use this lens 'll auto focus option enabled in taking image?

Yes, this will autofocus.AF-S means there's a motor build into the lens (sigma calls it HSM). VR means it's optically stabilized. 18-55 is the zoom range. Play a bit with this tool to get a feel for that: http://www.tamron-usa.com/...arison.php

The D5100 is an SLR, so there's not going to be any kind of auto focus on any DSLR camera. But the Lens does have an auto-focus on it.

That's a decent camera too. Nikons tend to have better lenses in my opinion, but Canon is going have better software on their SLRs.

AF-S means autofocus silentwave motor. Which means the focus motor is built into the lens itself.
18-55 is the focal range when you take the ratio 55/18=3+ which gives you a 3x optical zoom. VR stands for vibration reduction which is a good feature but not so much for a short lens like the 18-55mm. It's is very much useful for telephoto lens as it eliminates the shake at the tip of the lens and give you sharper images at full zoom.

When you see "AF-S" as part of a Nikon lens description you can be sure it will auto focus on your Nikon D5100.

18mm is the wide-angle end of the zoom.
55mm is a short telephoto end of the zoom.
VR is for "Vibration Reduction" which is Nikon's name for Image Stabilization.

Contrary to what "DMM 1984" said, Sony and Pentax DSLR cameras have a focusing motor in their camera bodies. Sony and Pentax also have their respective versions of Image Stabilization in their DSLR camera bodies.