The electronic configuration of Mg is
$1{\mathrm{s}}^2,\mathrm{}2{\mathrm{s}}^2,\mathrm{}2{\mathrm{p}}^6,\mathrm{}3{\mathrm{s}}^2,\mathrm{}3{\mathrm{p}}^0$
In it 3s – orbital is completely filed and 3p-orbital is empty. There is very small energy difference between 3s and 3p – orbitals. Thus, they overlap and make the Mg a conductor.

Band model of Mg