First of all let's make clear that these so-called constants are in fact functions of temperature and frequency but for simplicity of calculation one can consider they remain approximately constant for a given (and limited) temperature and frequency domain.As you know the dielectric constant is related to a material's capacity of modifying electrical flux density by phenomena such as polarization -a mere orientation of molecules - or dissipation losses as heat, etc.  So the dielectric "constant" is just the ratio of the capacitance value for ideal capacitors one having the material as dielectric and the other one void between their identical plates. 

These phenomena are material-dependent because the forces necessary to orient molecules at the expense of the electrical field passing through the material have to overcome different structural cohesion electrostatic, van der Waals forces, etc caused by different "layouts" of different materials. These phenomena are also frequency dependent because all of these electric dipoles created by the electrical field in the material have various oscillation frequencies, and as they are brought closer to resonance the polarization phenomena takes precedence over dissipation phenomena so the so-called "constant" appears to increase slightly while at high frequencies the opposite is true.

The "static" dielectric constant is simply the dielectric constant related to the material behavior in low frequency or constant  electric fields, while high frequency "constant" should be by now self-explanatory. The difference is ..well- the material behavior, hence the numeric value... So to sum up: at high frequencies, you may encounter some insulators that start acting up strange, such as increasing losses in signal by  heating and "stealing"/flattening-distorting your signals ,because of the mechanisms discussed above,  and some insulators that for example do not distort or attenuate significantly; you may find unacceptable losses in some capacitors with dielectrics not suited for high frequencies and not so serious ones in high frequency capacitors..and so on.The phenomenon is extensively used in power supply filtering when naturally occurring high frequency rectifier noise is passed through large electrolytic caps that are not suitable to pass high frequencies, so they dissipate- and thus eliminate- the noise by heating up ...

So on the basis of these high frequency behaviors materials are used in various applications and avoided in others. Same precautions with temperature- some materials change dielectric behavior when heated or cooled.

Agreeing with the previous poster (of course), i would add that there are different mechanisms of polarization that a material can use. LINK: http://www.doitpoms.ac.uk/tlplib/dielectrics/polarisation_mechanisms.php

Some mechanisms are fast, but not so strong (atomic/electronic), some are slow, but stronger (ionic). Some molecules, like water, are of themselves dipoles and can therefore orient the molecule to oppose the electric field (for water that goes at medium speed, medium strength).

If you then look at the dielectric constant vs frequency plot of a material you see it change with frequency

https://en.wikipedia.org/wiki/Permittivity#/media/File:Dielectric_responses.svg from the wiki page: https://en.wikipedia.org/wiki/Permittivity

For water we can explain this as follows: if you add salt and use low frequencies the ions will orient themselves against the electric field. If you add a lot of salt the apparent dielectric constant of water actually goes up so high that you can consider the water as an electrode. Also, the more salt you add, the higher frequency the ionic polarization can handle. At some frequency (order of 100 kHz) however, ions cannot move fast enough. At this point the fastest polarization is the orientation of the water molecule (dipolar). This gives the well known value of 80 for the relative permittivity of water. The water molecule will however not be able to follow frequencies over a few 100 Mhz. (One of the reasons why microwave ovens work at 1-3GHz). After that the electronic and atomic polarization methods kick in.

Defnitely you should browse that University of Cambridge link. It helps in the understanding a lot.

Kind regards,

Arjen Pit

The colleagues above described the dielectric constant in detail. However, i would like to add some comments regarding the necessity of introducing the dielectric constant. 

The electrical properties of materials are determined by their response on the application of an electric field E. So, the electrical materials are classified according to this response into conductors, insulators and semiconductors. The ability to conduct current is measured by the conductivity sigma, of the material according to the Ohm s law:

j= sigma E,

sigma which is a material property is the ratio of the current density J to the applied electric field.

By inspecting the material it is found that its electrons may be classified into free electrons and tied bound electrons. The free electrons affect the conduction of the material and determines its conduction.

It is found that the bound charges in the material are affected by the electric field in the sense of displacing the positive charges from the negative charges for small distances and form which is called electric dipoles as the colleagues explained in the previous posts. This polarization effect is described by the dielectric constant epsilon such that the electric displacement D= the electric flux density = epsilon E,

So, the dielectric constant is a material property and it is determined by the ratio the displacement D to the applied electric field.

The dielectric constant as a dielectric material property depends on the frequency and temperature of the material.

wish you success

Thank you all 

  Dear Showkat,

   If you have a dielectric medium,i.e. formed by important electric dipoles, which is electrically neutral and bad conductor given the electronic localization. Then when you apply on it an electric field, the dipoles align with the field without translate, but that takes a time (relaxation time t) and if the electric field oscillates at a frequency f with one time of oscillation lower than the relaxation time, it means that part of the electric field doesn't employ all its energy in the change of the electric polarization: this term enters as an imaginary electric permittivity responsable of the losses under an ac field, in a similar form of the concept of reactance for the impedance generalizing the stationary resistence one . In such a case, the electric permittivity might be calculated using the Debye mechanism

             ε(ω)= εf + Δ ε/(1+iωt)

  where Δ ε= ε0- εf is the difference between the ε0 permittivity under a static electric field and  εf the permittivity under an electric field dependent of high frequency.

   Thus you can see what is the relationship between stationary and oscillatory high frequency dielectric constants in a simple form which also provides you with the losses (heating) associated with the dielectric material.

The dielectric constant is critically important to getting accurate depth readings with GPR systems. Dielectric constants, also known as relative dielectric permittivity, are measured on a scale of 1 to 81, where 1 is the dielectric constant for air (through which radar waves travel most quickly) and 81 the constant for water (through which radar waves travel most slowly).