When a colour is measured using the CIE system it can be defined in such a way that it can be reproducted exactly. This is because the CIE system defines the conditions and mechanism of the measurement of a colour, for example the exact type of illumination and geometry is specified. However, even though a colour has set CIE co-ordinates, it will still appear to an observer to be different as its surround or the ambient lighting change. This has serious consequences for digital colour spaces. For example when printing the conversion from RGB to CMY(K) may be perfect but the viewing conditions of the screen and hard copy will be different. The display may have a white point of around 8000k with ambient lighting provided by fluorescent tubes while the print may by displayed in a tungsten lit gallerey - oh dear! So although you may have a colour match in terms of CIE co-ordinates, the colours may appear to differ.
The solution is to use a colour appearance space. An appearance space can be used to predict the appearance of colours under a variety of different viewing conditions. An example is Hunt's model of colour vision, described in both Measuring Colour and the fifth edition of The Reproduction of Colour.