The atoms of solid sodium are bound together through metallic bonding, which involves the presence of delocalized electrons around positive ions of sodium. The delocalized electrons can carry an electric current, thus allowing solid sodium to conduct electricity.
Sodium is a metal. Its outermost shell or energy level has only one electron. Each sodium atom is surrounded by eight other sodium atoms, each of which has one electron in its outermost energy level. The close proximity of the atoms in solid sodium leads to the sharing of space between the atoms and therefore the sharing of the outermost electrons. The central sodium atom shares electrons with its eight neighbors and each neighbor in turn shares electrons with its eight neighbors and so on.
The electrons are able to detach themselves from their parent atom and move around freely. They are said to be delocalized electrons. Each sodium atom becomes a positive ion, having lost its outermost electron to delocalization. The metal retains a solid structure due to the electrostatic force of attraction between the positive sodium ions and the delocalized electrons.
Conductors allow the free flow of electrons through them. Since sodium has electrons that are free to move, it is a conductor of electricity.