How do dslrs such as nikon 3100 zoom?

Well do dslrs have zoom. And what is the lens in mm mean what do the lens mean.

Added (1). Ya i'm sorry, the lens zooms. What i meant was that is there any optical zoom in dslrs. What is the optical zom in d3100 is it 3x! If i'm not wrong

It's the lens that zooms, not the camera.mm is the focal length of the lens.

That's true. The lens zoom has nothing to do with the camera. There's a real large selection of lenses, some very expensive some not so bad. Here's a good place to do lens research.
http://www.bhphotovideo.com/...video.com/

3x is a ratio of the shortest focal length compared to the longest focal length. Being a ratio is is relative to the lens.

Basically multiply the short focal length by 3 to get the long focal length.

So a 3x 50mm lens would be 50-150mm. And a 3x 11mm lens would be 11-33mm, and so on.

Your kit lens is a 18-55mm lens, so it is also a 3x 'something lens (18mm x 3.05 = 55mm).

All three above answers are absolutely correct. The zoom factor is found in the lens, not the camera. That's like asking if a certain car has the right treads for snow or wet weather. The tread is a factor of the tires, not the car.

That being said, you can have a zoom of zero, with a prime lens like the 35mm f/1.8.
You can have a zoom of 2x, with a lens like the AF-S 200-400mm.
You can even get up to 15x with the Tamron AF 18-270mm.

As far as what the "mm" means, that's the basic measure of the power of the lens power. On a DX camera like the D3100, a 35mm lens give you the equivalent of the normal human eye. A smaller mm number backs away and shows you more of the scene. A larger mm number brings subjects closer.

Use this Nikon lens simulator to let you see what different mm lenses look like though your viewfinder.