Dan - claying removes contaminants from the clearcoat that cannot be removed with polishing. Without claying, they'd be there permanently. Claying gently removes them, for when you clay the paint, it pulls them from the clearcoat, as they'd rather stick to the clay than the paint.

This gives a perfectly smooth, glass like finish to work on - it's easy to identify a car that's been clayed just by touch; they're noticably smoother than a non clayed car, even if it's been polished and waxed. In turn, this means all the products you use after the clay, starting with a polish, work to the maximum of their abilities, as they're not pulled about by the surface contaminants.

Gareth