A device dependent colour space is a colour space where the resultant colour depends on the equipment and the set-up used to produce it. For example the colour produced using pixel values of rgb = 250,134,67 will alter as you change the brightness and contrast on your display. In the same way if you swap your monitor the red, green and blue phosphors will have slightly different characteristics and the colour produced will change. Thus RGB is a colour space that is dependent on the system being used, it is device dependent. A device independent colour space is one where the coordinates used to specify the colour will produce the same colour wherever they are applied. An example of a device independent colour space is the CIE L*a*b* colour space (known as CIELAB and based on the human visual system).
Another way of looking a device dependency is to imagine an RGB cube within a colour space representing all possible colours (for example a CIE based colour space). We define a colour by the values on the three axes, however the exact colour will depend on the position of the cube within the perceptual colour space, move the cube (by changing the set-up) and the colour will change. Some device dependent colour spaces have their position within CIE space defined, these are known as device calibrated colour spaces and are a kind of half way house between dependent and independent colour spaces. For example, a graphics file that contains colorimetric information, i.e. the white point, transfer functions, and phosphor chromaticities, would enable device dependent RGB data to be modified for whatever device was being used - i.e. calibrated to specific devices.