Kilogram Exponent (KGE) is the exponent used in the calculation of Relative Power. KGE is determined based on gradient of the terrain. In general, lower values indicate descending terrain whereas higher values indicate steeper grades. Note that when KGE = 1, the exponent essentially makes Relative Power the same as Watts/KG whereas when KGE = 0, the exponent essentially makes Relative Power the same as Watts. In other words, the steeper the gradient, the more the weight of the rider comes into play. The flatter the terrain, the less weight impacts performance.
Interestingly, the effect of a reduction of 1kg of body weight can be calculated quite simply:
Increase in Relative Power per kg = watts/kg * KGE
As an example, reducing weight by 5kg where KGE = 0.5 at 375W for a 75kg rider, is 5*375/75*0.5 = 12.5W.
Recently, a new metric called Compound Score (read about it here) multiplies Watts and Watts/kg. Mathematically, this equates to a KGE of 0.5.