The best current theory of superconductivity (which is certainly not the last word, as it doesn't adequately account for high-temperature superconductors) essentially explains it as a coupling effect between electrons and phonons; grossly oversimplified, the conduction-band electrons can't scatter off atoms (which, microscopically, is how resistance happens) 'cause there aren't any open states of the right energy in the phonon bands (bouncing an electron off an atom causes mechanical vibrations... that is, creates a phonon).
Oh, one other thing...