One important property of a dielectric material is its permittivity.  Permittivity (ε) is a measure of the ability of a material to be polarized by an electric field. 

It is, however, easier to grasp the concept of permittivity by first discussing a closely related property, capacitance (C). Capacitance is a measure of the ability of a material to hold charge if a voltage is applied across it, and is best modeled by a dielectric layer that's sandwiched between two parallel conductive plates. 

If a voltage V is applied across a capacitor of capacitance C, then the charge Q that it can hold is directly proportional to the applied voltage V, with the capacitance C as the proportionality constant.  Thus, Q = CV, or C = Q/V.  The unit of measurement for capacitance is the farad (coulomb per volt).

The capacitance of a capacitor depends on the permittivity ε of the dielectric layer, as well as the area A of the capacitor and the separation distance d between the two conductive plates.  Permittivity and capacitance are mathematically related as follows:  C = ε (A/d).

When the dielectric used is vacuum, then the capacitance Co = εo (A/d), where εo is the permittivity of vacuum (8.85 x 10^-12 F/m).

The dielectric constant (k) of a material is the ratio of its permittivity ε to the permittivity of vacuum εo, so k = ε/εo.  The dielectric constant is therefore also known as the relative permittivity of the material. Since the dielectric constant is just a ratio of two similar quantities, it is dimensionless. 

Given its definition, the dielectric constant of vacuum is 1. Any material is able to polarize more than vacuum, so the k of a material is always > 1. Note that the dielectric constant is also a function of frequency in some materials, e.g., polymers, primarily because polarization is affected by frequency. 

A low-k dielectric is a dielectric that has a low permittivity, or low ability to polarize and hold charge.  Low-k dielectrics are very good insulators for isolating signal-carrying conductors from each other.  Thus, low-k dielectrics are a necessity in very dense multi-layered IC's, wherein coupling between very close metal lines need to be suppressed to prevent a degradation in device performance.

A high-k dielectric, on the other hand, has a high permittivity.  Because high-k dielectrics are good at holding charge, they are the preferred dielectric for capacitors.  High-k dielectrics are also used in memory cells that store digital data in the form of charge.