Delta-E (dE) is a single number that represents a difference between two colours, with the basis that a dE of 2.3 is the Just Noticeable Difference (JND), or smallest colour difference the human eye can see.
So, theoretically any dE less than 2.3 is imperceptible, while any dE greater than 2.3 is noticeable. However, some colour differences greater than 2.3 can be imperceptible, while some colour differences below 2.3 can be very visible, depending on the colour being measured.
Additionally, and more importantly, when Delta-E is used to represent calibration accuracy it is normal to only report a limited number of colour points. Usually the grey Scale and RGB primary colours only are represented, as shown above, or a small selection of colours based on something like the Macbeth Colour Checker. Neither is good enough in reality, as far too few points are being used to try to verify the total volumetric colour space.
Note: Although a dE of 2.3 is regarded as the technical JND value, many refer to a value of 1.0 as being a more realistic threshold for imperceptible difference.
If you have a perfectly linear display (with perfect RGB Separation, and therefore zero cross-coupling errors), you could actually profile just the grey scale, and single patch RGB readings, and then generate a perfect 3D LUT that would control not just the grey scale, but total gamut (all the colours) as well. Very few calibration system understand this fact.
But, as few displays are truly linear in response - with the output changing directly in line with any input change - it's a concept that cannot really be used.
Notice the use of 'profiling' and 'calibration' as separate functions - this is of critical importance for accurate final calibration. See later.