Electrical insulation is the absence of electrical conduction. Electronic band theory (a branch of physics) says that a charge will flow if states are available into which electrons can be excited. This allows electrons to gain energy and thereby move through a conductor such as a metal. If no such states are available, the material is an insulator.
Most (though not all, see Mott insulator) insulators have a large band gap. This occurs because the "valence" band containing the highest energy electrons is full, and a large energy gap separates this band from the next band above it. There is always some voltage (called the breakdown voltage) that will give the electrons enough energy to be excited into this band. Once this voltage is exceeded, the material ceases being an insulator, and charge will begin to pass through it. However, it is usually accompanied by physical or chemical changes that permanently degrade the material's insulating properties.
Materials that lack electron conduction are Glass Insulators if they lack other mobile charges as well. For example, if a liquid or gas contains ions, then the ions can be made to flow as an electric current, and the material is a conductor. Electrolytes and plasmas contain ions and will act as conductors whether or not electron flow is involved.
Insulators suffer from the phenomenon of electrical breakdown. When the electric field applied across an insulating substance exceeds in any location the threshold breakdown field for that substance, which is proportional to the band gap energy, the insulator suddenly turns into a resistor, sometimes with catastrophic results. During electrical breakdown, any free charge carrier being accelerated by the strong e-field will have enough velocity to knock electrons from (ionize) any atom it strikes. These freed electrons and ions are in turn accelerated and strike other atoms, creating more charge carriers, in a chain reaction. Rapidly the insulator becomes filled with mobile carriers, and its resistance drops to a low level. In air, "corona discharge" is normal current near a high-voltage conductor; an "arc" is an unusual and undesired current. Similar breakdown can occur within any insulator, even within the bulk solid of a material. Even a vacuum can suffer a sort of breakdown, but in this case the breakdown or vacuum arc involves charges ejected from the surface of metal electrodes rather than produced by the vacuum itself.