Digital camera sensors, the electronic parts that capture images, come in a variety of sizes. Inexpensive cameras use small sensors, and higher end cameras typically use larger sensors. When a manufacturer uses a sensor that can reproduce an image equivalent in size to a 35mm film camera frame, the sensor is called a full-frame sensor. In Nikon terms that sensor is called FX.
For cameras with smaller sized sensors, the sensors are known as "cropped". And, just as in post processing the cropped sensor provides the effect of zooming in on the subject. One of the popular Nikon cropped sensors is called DX. A DX-sensor equipped camera provides a crop or zoom factor of about 1.5.
Why does any of this matter? As sensors get smaller for less expensive cameras, either the number of sensor elements has to go down, or the size of the elements has to go down to fit in the same space. As the size of the elements go down, the overall sensor becomes less sensitive to light. You may end up with a high mega-pixel camera that only takes pictures in bright light. On the other hand cameras with large sensors can use relatively large sensor elements, which are more sensitive to light, and therefore, work better in low light conditions. A second reason this matters is wide angle lenses lose their apparent wide-angles by the crop factor, e.g on a DX-sensor 18mm becomes 27mm. On the other end of the scale, telephoto lenses gain a little reach, e.g. on a DX-sensor a 200mm lens becomes zoomed (cropped) to 300mm.
Camera lens manufacturers build lenses to take advantage of the different type sensors. As a result and practically speaking, price and performance of cameras and lenses are the trade-offs for the different sized sensors.
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