What is the difference between a DX and FX?

I've noticed that in Nikon's len's line up there are DX and FX lenses.

What is the difference between the two?
I know that DX cameras can take all lenses but FX cameras can't.

What type of cameras are DX and are they better for being able to take all lenses?
Which type of camera would be at the higher end?

FX is the higher end.

FX cameras uses a sensor of the same size as old 35mm film, or they use actual film. They need lenses that will cover the whole area of such a relatively large sensor.

DX cameras use a smaller sensor. They can use FX lenses as they simply grab a part out of the middle of the image projected by those lenses. DX lenses on the other hand are designed to fill merely the size of a DX size sensor. They won't be able to fill the whole frame on FX cameras, but they cost less than FX lenses.

Since DX cameras basically "crop" a part ouf of the center of the frame, compared to FX ones, they have that so-called crop factor. When mounted on a DX camera, the focal lengths of lenses appear to be as they would if they were 1.5 times that value on a FX camera.

So a 50mm lens on a DX camera would work just like a 75mm one on a FX camera.

Note that for this factor the type of the camera is important. Lenses too are designated as FX or DX, but that has nothing to do with the crop factor, it merely answers the question if they can fill a full FX frame or not. So a 50mm FX lens will work on a DX camera just like a 50mm DX lens would. 50mm remains 50mm when it's mounted on the same camera, regardless of the type of the lens.

FX is full frame, sensor is the same size as 35mm film frame (higher end).
DX uses a sensor smaller than a FX.

In the Nikon lineup, a DX camera body can use DX and FX lenses.
A FX camera body can also use DX and FX lenses. If you use a DX lens on a FX body, the camera will know this and only use a cropped portion of the sensor equivalent to a DX sized sensor to reduce vignetting.

DX cameras: Anything under $2000 like the D40, 50, 60, 70, 80, 90, 300, 3000, 3100, 5000, 7000.
FX cameras: Anything over $2000 like the D700, D3.