K-value
Firstly, K-value indicates the ability of a material to conduct heat. Materials with low thermal conductivities do not easily allow heat energy to pass through. Normally, you would look for a material with a low K-value to insulate, as this will keep the cool inside your building.
R-value
R-value refers to a material’s ability to resist heat transfer at a certain thickness. When looking for a material to insulate your building you would generally look for a material with a high R-value, and therefore, one that can resist heat transfer well. While K-value deals solely with just the material, R-value refers to the material and its thickness.
U-value
U-value assesses the rate of heat loss through a given thickness of a building element (roof, wall or floor). Ideally you would want a material which gains a small amount of heat in any given time, so you would want the U-value of a material to be low. When referring to the U-value of a building the R-value of all its different components will be considered.