Non-conductors of electricity are also known as insulators. Insulators do not allow a significant amount of electrical current to flow through. Some examples of insulators are glass, rubber and plastic.
Materials can either be insulators or conductors. Conductors have a low amount of resistivity, which means electrons can flow through them without much impedance. Most conductors are metals, although there are exceptions.
Having a small amount of valence electrons means that metal atoms are always trying to give away electrons. This property allows electrons to move from atom to atom very efficiently. In insulators, atoms do not want to give away electrons, which halts electron flow.