Why are metals conductive in terms of orbitals?
It's not that the electrons are completely unbound from the atoms - they still attract each other and form the bonds with other atoms. But the attraction between the atom and its electron is pretty weak so it's easy to detach the electron from the atom.

The properties of the metals are better to be described via ionization energy - the energy needed to remove an electron from an atom. Elements to the right of the periodic table have high ionization energy - they are not willing to lose electrons. Therefore these elements are bad conductors (and are not metals).

Metals have lower ionization energy - their valence shell just started to be filling and the strength of the proton is not enough to keep them tight. Therefore these electrons are free to flow with minimum efforts applied - which would form electrical current.

The intention of the "sea" model is to describe (in simplified manner) the fact that electrons are floating around from one atom to another. And while they participate in bonding, this is a dynamic structure that breaks and forms all the time. 

Here is a nice video from Khan Academy on the metallic nature.