Difference between dielectric constant and dielectric function I'm confused by the definition of dielectric constant. We all know that dielectric is function of wavelength, because materials respond in different ways depending on the energy of the light. But what does it mean when it says 

Dielectric constant of a material is = 5. ?

 A: Dielectric constant is a measure of how a material responds to an electric field, particularly how much separation of charge occurs. 
Simplistically, electrons can be thought of as bound to nuclei with springs. Or perhaps positive and negative ions bound with springs. An electric field pushes positive and negative charges in opposite directions. 
The dielectric constant is a measure of the spring constant. A material with a large dielectric constant is made of "stretchy" atoms or molecules. 
Given a parallel plate capacitor, the capacitance depends on the distance between the plates. Inserting a dielectric effectively adds plates, reducing the separation.  
      Capacitor                  Dielectric
   +++++++++++++++             
                               +- +- +- +- +-

                               +- +- +- +- +-

   ---------------

   Capacitor with dielectric   
   +++++++++++++++             
    -  -  -  -  -
    +  +  +  +  +

    -  -  -  -  -
    +  +  +  +  +
   ---------------

The effect of an oscillating electric field depends on frequency. Masses and springs have resonances. The dielectric constant is large near resonance frequencies. So you can learn things about atomic bonds from the dielectric constant. 
A: Dielectric constant is a complex number. It is a function of state variables, electric field, frequency, temperature, pressure, mechanical stress, etc. Because of this the value listed in a data sheet should indicate the condition of measurement. Usually it is measured at 1kHz because on inexpensive meters available performing measurement at this frequency.
A: It means that when this slab is introduced in a capacitor(covering it fully), its capacitance increases by a factor of 5.
A: When one reads a statement, " dielectric constant of SiO2 is 5" It is the response of SiO2 to a dc electric field, which is normally measured like a capacitor.
But then you probe the material with light (varying electric field) We get the ac response, like an elipsometery measurement 
A: You can speak of a dielectric constant when the dielectric function is approximately constant for the given range of interest. Some materials, like air, have a slowly varying function with the wavelength; in that case, you can consider it constant.
Also, if your problem involves a fixed wavelength (say, you consider the influence of a laser on a material), then naturally you can also speak of a dielectric constant.
