What specific property of metals accounts for their unusual electrical conductivity?

The conductivity of metals is due to the electron configuration of these atoms. They generally have fewer valence electrons than valence orbitals, so that empty orbitals in the valence shell exist.

In a solid crystal of #N# metal atoms, these half-filled orbitals and empty orbitals overlap to create a network of #N# interconnected orbitals. The exclusion principle still requires that all these orbitals have slightly different energies. As a result the orbitals change slightly to become a group of #N# molecular orbitals that have very similar energies. Since the orbitals are so close in energy, we think of them as a continuous band of energy levels.

This creates a situation in which valence electrons occupy a portion of these orbitals, but because there were more orbitals than valence electrons, there will also be a band of empty orbitals at nearby energies.

All that remains is for a small energy application, such as a voltage applied to the crystal to cause the valence electrons to jump into one of the orbitals in the empty orbitals. These electrons will be able to move easily among the many empty orbitals that link the metal atoms together.

Viola! We have electrical conductivity.

Here is a source that I think explains this topic quite clearly. Check it out:

http://xbeams.chem.yale.edu/~batista/vaa/band.html