Nd
As mentioned in the Maxwell Materials page, the Nd is the index of refraction of the material. The name Nd is used because it is the common way to denote an index of refraction that has been measured at the wavelength of 583 589.3 nm for a certain material. You can find a list of common IOR values here. The Nd is important not only for transparent materials but for all materials as it defines both surface reflections and the refraction of light inside the object.
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The Nd has no influence on the look of the material when working with Lambertian materials. Lambertian is a special mode which makes a surface reflect all light in a diffuse way (its roughness is 100). It is the highest roughness a surface can have. It is also important to remember that the Nd has less influence on the reflectance of an object the higher you set the Roughness and instead it's the Reflectance colors that matter more and more. You will see the biggest changes to the reflectiveness of the object as you change the Nd, when the surface roughness is low.
K parameter
From a physical point of view, the index of refraction is not just a plain number. In fact it is a number derived from a complex calculation to define the refractive index at one particular wavelength. This is the calculation:
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The Nd represents the refractive index, which is the well-know concept of Index of Refraction we often use.
The K is the extinction coefficient: the amount of absorption loss when an electromagnetic wave propagates through a material. This is usually confused with the Abbe, but it is not related to this. K is related to the extinction of the wave.
The use of the K value is optional. In most situations it is enough to just use the Nd value. Only in specific situations where the extinction effect is important, is it necessary to use the K parameter to get a more precise result.
The values of the extinction coefficients are obtained from measurements in laboratory, and are also included in the IOR files.