The dielectric permittivity of an insulating material is a measure of its capacity to store electrical energy when placed under a voltage (electric potential). It is typically cited after being converted into the relative permittivity or dielectric constant (the latter term being more common in industry), which is the unitless ratio of the material's permittivity to that of free space.
It is not measured for electrically conductive materials.
The value may vary with AC frequency. It does not vary with specimen thickness or voltage magnitude, so long as the voltage is less than the material's dielectric strength.
High permittivity is desired in capacitors. Low permittivity is preferred in electrical insulation.
Dielectric permittivity is also called electric permittivity and electrostatic permittivity. In effect, any use of the term "permittivity" in the context of materials and electricity will likely refer to the same thing.
The main international testing standard is IEC 60250, which covers all insulating materials. There are also ASTM testing standards, including D150 for solid electrical insulation, D2149 for ceramics, and D3380 for polymeric microwave circuit substrates.