Q: What is an Insulator?
A: Insulators are any materials whose internal electric charges do not flow freely and therefore resist the flow of current. Current likes to flow in materials that have electrons which can easily gain energy and freely move about (as in metals). Insulators are necessary to protect a circuit from a dead short to ground. There are many forms of insulation and each one carries their own dielectric constant, which is the material’s measured value of resisting flow and it’s capability of being polarized. A true dielectric is an insulative material in which the atoms are free to rearrange themselves and thus become polarize when in the presence of an electric field. This is how capacitors work. The dielectric insulation sandwiched between the plates encourages the negative particles to accumulate in the + end of the dielectric while the – charges are repelled from the - side of the dielectric, leaving only the positive charge on that plate.
Most insulators have a large band gap. This is the energy range in a solid where no electron states can exist. This gap occurs because the "valence" band containing the highest energy electrons is full, and a large energy separates one band from the next band above it. There is always some voltage (called the breakdown voltage) that gives electrons just enough energy to be excited into this next band. Once this voltage is exceeded the material ceases being an insulator, and the charge begins to pass through it.
The primary purpose of insulation in a cable is simply to prevent the wire from short circuiting while also sealing the conductor from the air and environment.