CIE XYZ:

The basic CIE colour space, or colour model, is based on a 'Standard Observer and 'Standard Illuminants' (D50, D65, etc.). This is a numerical model of colour sensitivity based on research commenced in the 1920s on a sample of people with normal colour vision. It is a 'universal colour space' representing the colour spectrum visible to the 'average human'. The light-sensitive retina at the back of the eye has three types of receptors near the centre, known as cones. They are sensitive to the three primaries, 'red, green and blue'. The CIE XYZ tristimulus values are assigned to the red, green and blue curves respectively. These approximate to the cones in the eye. The relative response of each is plotted on a diagram against the wavelength in nanometers. The eye also has rods, outside of the retina's centre, which are sensitive to low-wavelength light and which only operate at low levels of illumination. There are two axes: vertical and horizontal.

The vertical axis represents Relative Response 0 - 2.0 (shown here) or Reflective Intensity 0 - 120% (not shown).

The horizontal axis represents Wavelength in nanometers, usually from about 380 to about 720nm.

It should be emphasized that this is a 'device-independent' colour space in which each primary colour (X,Y,Z) is always constant, unlike  RGB which varies with every individual device (monitor, scanner, camera, etc.). XYZ is typically used to report the spectral response of a sample measured by a colorimeter or a spectrophotometer. A colorimeter may contain as few as three sensors, one each for red, green and blue, (or X, Y and Z), and will typically be used for display calibration and profiling. A spectrophotometer will report the entire spectral response at frequent intervals along the spectrum, say every 10 nanometres, and will typically be used to measure printed sheets to control a press or create an ICC profile.

While CIE XYZ is used to report colour from measuring instruments, it is not so useful for humans to describe colour. Another use is as the Profile Connection Space (PCS) within an ICC profile, where it may be used instead of CIE Lab.

You may notice that the Y ('green curve') covers the widest wavelength. This corresponds to the overall human visual response to all colours, or lightness. It is therefore also used to indicate luminance ('lightness').

CIE L*a*b*: In such case the vertical L* axis represents Lightness, ranging from 0-100.  The other (horizontal) axes are now represented by a* and b*. These are at right angles to each other and cross each other in the centre, which is neutral (grey, black or white). They are based on the principal that a colour cannot be both red and green, or blue and yellow. 

      The a* axis is green at one extremity (represented by -a), and red at the other (+a). The b* axis has blue at one end (-b), and yellow (+b) at the other. 
The centre of each axis is 0. A value of 0, or very low numbers of both a* and b* will describe a neutral or near neutral. In the case of paper, the white point in terms of a* and b* is usually carried through to the black, being gradually reduced towards '0'.

In theory there are no maximum values of a* and b*, but in practice they are usually numbered from -128 to +127 (256 levels).

The CIE Lab colour model encompasses the entire spectrum, including colours outside of human vision. CIE Lab is extensively used in many industries apart from printing and photography. Its uses include providing exact colour specifications for paint (including automotive, household, etc.), dyes (including textiles, plastics, etc.), printing ink and paper.