Most dSLRs in the market now can be roughly divided into 2 groups: those with crop sensors, and those with full frame sensors. For Nikon, this is represented by “DX” for crop sensors and “FX” for full frame sensors.
Full frame sensors are also known as 35mm sensors. They are of the same size as the 35mm sensors in the past during the days of film cameras.
Crop sensors are also known as APS sensors and are smaller than full frame sensors. Hence, in terms of the 35mm sensors, there is a “magnification factor” for the smaller APS sensors. For Nikon DX cameras, the factor is 1.5x and for Canon cameras, it is 1.6x. In other words, full frame 35mm sensors are 1.5 times bigger than Nikon’s DX cameras and 1.6 times larger than Canon cropped sensor cameras.
Another important point to note with regards to your lenses is that, the focal length that you see on your lenses are what you get ONLY when you attach them to full frame cameras. It does not matter whether your lenses are DX or FX lenses. All markings on them refer to focal lengths that are obtained on FX cameras as they are taken as the standard.
Here is where things get a little complicated.
If you attach a DX lens, for instance 18-55mm, onto a DX camera, you need to apply the 1.5x calculation to all focal lengths to obtain the effective, or “actual” focal length, when you look through the viewfinder. This means that in full frame 35mm terms, you get a 27-82.5mm lens instead of 18-55mm. However, if you attach the same lens to a FX camera, you get 18-55mm.