DX and FX denote the image sensor size in a camera, which records the scene when you capture a photograph. It is the most expensive part of a digital camera and the whole camera is built around it.
FX is also known as full frame sensor and DX is known as cropped sensor. DX camera are cheaper and lighter than FX cameras. DX image sensor is about 50-60% of the size of a FX image sensor. Think of it as a hole in a cardboard box through which you are peeping. The bigger the hole (image sensor) the bigger is your view-able area. Size of the DX sensor depends on the manufacturer. If it’s size is 40% of that of FX, then it comes with a crop factor of 1.6. For example, if you’re using a 50mm lens in a DX camera with crop factor of 1.6, then the resulting lens will be of,
50mm x 1.6 crop factor = 80mm lens
100mm lens becomes 160mm lens
50mm lens becomes 80mm lens
and so on.
Expensive cameras have large FX sensors which have no crop factor. FX camera’s produce images that are less noisy and better lit because of its high sensitivity to light.
Each lens is made in order to cast a circle on the camera’s sensor. As DX is smaller than FX, the circle casted on the sensor by DX is smaller as compared to FX lens.
The advantage that DX cameras have over FX is that they can work perfectly with both DX as well as non-DX lenses. However, you may use a DX lens with FX camera too, but it will come with a vignetting effect in the photographs.