In very basic terms, it tells you how "good" a pipe insulation is (although it is not always the only consideration).
The scientific description of thermal conductivity is as a measure of a materials ability to conduct heat. In other words, the lower this value is the better it is as an insulation in terms of preventing the transfer of heat.
The thermal conductivity, or k value, is commonly expressed when talking about insulation in W/m.K (sometimes written as W/(m.K) ) which is an abbreviation for Watts (per Metre) in Kelvin. In other words, it is the rate of heat flow (measured in Watts), per metre, at a given temperature (Kelvin being a measurement of heat).
You will see this is generally expressed next to a temperature when referring to pipe insulation, usually in degrees centigrade. This is because the temperature effects the rate of heat transfer. The greater the difference in temperature between what is inside the insulation and what is outside the insulation then the higher the thermal conductivity will be.
So, what does all of this mean to you if you are looking at a pipe insulation product?
Generally speaking for domestic applications you will be looking at flexible pipe insulations - and there is little to distinguish between them in terms of insulation quality. Eurobatex Class 0, Armaflex Class 0 and Climaflex are each as efficient as the other in terms of thermal insulation values (NB This is not the only factor as you may also need to consider the fire rating, whether you want split or unsplit, and whether or not you require something that is self-seal).
In terms of foil faced insulation products there is a bit more of a distinction to make. Phenolic Foam (eg Kingspan Kooltherm ) is the most efficient product group for insulation, and in most case you are able to use a thinner wall thickness to achieve the same results as you could with a mineral fibre (eg Sager Glass Wool or Rockwool Rocklap). So, for example, in a heating pipe situation you might find that 15mm of phenolic would achieve a similar result to say 20mm of mineral fibre.
You must be much more careful though with HVAC work as the choice is not solely based on the materials thermal values - you must also consider its mechanical properties, cell structure and temperature limits when selecting a product.
Hopefully this little article has been useful in explaining what a thermal conductivity is - feel free to leave a comment if you have any questions.