Conduction metallic

Electricity is movement of charge
A substance conducts electricity, if when the substance is placed between the electrodes in a circuit which includes a source of electrical current, the circuit is complete due to electricity flow through the substance.
 
In electronic conduction the charge is carried by electrons.
 
Metals can be viewed as cations surrounded by a sea of electrons
The video below shows this model of metalllic bonding and the movement of electrons between the metal cations in the lattice.
 
liquid metal
conducts electricity
solid metal
conducts electricity


Electricity is conducted by solid metals due to movement of these electrons.

The diagram shows that the cations remain in place while electrons move from the negative electrode of the battery to the positive electrode.  This completes the circuit and causes the light bulb to glow.

The molten metal conducts electricity due to movement of the electrons.
  Note from the diagram that there is no net movement of the cations toward either electrode.