When electricity flows through a wire, it turns the atoms into ions by moving the electrons inside those atoms.
Copper is one of the best 'conductors' of electricity because its electrons are very easily moved from atom to atom. When a wire is connected to electricity it takes on a 'positive' and 'negative' end. The electrons will always want to flow from the positive end to the negative end. This movement of electrons works the same way in most materials, but more or less amplified depending on the availability of 'free' - or easily moved - electrons. It is also the reason for the feeling we get across our bodies when we get an electric shock.
While materials that are good conductors have an availability of electrons to move, those that are good insulators are the opposite and instead have an excess of protons. Things like plastic, glass and paper are good insulators.