Electrons move easily in metals but also move in other materials.
The delocalized electrons in metals allow electrons to move easily in metals. Metals have low electron negativity which means the metallic atoms do not have an high attractions for electrons. Each atom in the metallic crystal or matrix allows its electrons to be shared with the other atoms in the matrix. This creates what is referred to as a sea of electrons. So if more electrons are added to a metal the extra electrons are passed rapidly through the metal.
However metalloids are semi conductors. The atoms in silicon and graphite allow the electrons to move. The computer industry is based on the ability of semi conductors made of metalloids to allow electrons to move.
Salt solutions also conduct electricity. The water molecules split the ions in a salt into separate positive and negative charges. These ions can move electricity through the solution.