A non-rotating storm will have motion that is a sum of two components -- advection and propagation. For the advection part, imagine putting a leaf in a river. The leaf moves with the river -- so if the river is moving quickly, the leaf moves quickly as well. Of course, this is a simplification, but that's largely the advection term. The propagation term is a little more complicated. Consider a stationary thunderstorm cluster (so say there is no advection of the storm, or the mean wind of the cloud-bearing layer is 0). As the downdraft develops, a cold pool will develop at the surface (rain falling through subsaturated air leads to evaporation cooling, etc). This cold pool will spread out from the center of the downdraft, with the extent of the spreading being a fucntion of the degreee of low-level shear. If the cold pool is sufficiently deep to lift parcels to their LFC, air parcels will be forced over the cold pool and lead to new convection. The original storm will lose it's inflow, so the updraft weakens and, soonafter, the original downdraft weakens as well. So, in this regard, the storm has appeared to have moved, though it's really move of a old-cell-dies, new-cell-develops.
Depending on the storm mode and environment, the propagation component can be quite significant, and thus the reason we hear (and look out for) "forward-propagating MCS"). For a forward-prop. MCS, the line is both being advected by the mean wind AND propagating downstream, and it's largely for that reason why signficant winds are often associated with them.
Now, supercells (courtesy of their inherent rotating updraft) add in another factor for forward motion -- a contribution from perturbation pressure gradients. The presence of rotation leads to perturbation pressures, which lead to perturbation pressure gradients. This is the reason why you often see storms make a hard right-turn ("a right-mover") when they develop signficant cyclonic rotation / mesocyclones -- ther vertical pressure perturbations align themselves such that the storm is "pulled" to the right of its previous motion. In addition, the perturbation gradients also act to pull the storm "backwards" a bit (in nonscientific language). So, the net result is that for a cyclonically-rotating supercell in the northern hemisphere, the rotation of a supercell leads to a movement that is slower than, and to the right of, the mean wind.
For what it's worth, the opposite is true of anticyclonic supercells ("left-splits"). In this case, the perturbation pressure gradients align the opposite of that of a cyclonic supercell. For anticyclonic supercells, the perturbtation pressure gradients result in a motion that is faster than, and to the left of, the mean flow. Case in point: the left-split from the supercell down near McAlester, OK, on May 4th, 2003. This storm was moving NNW at 90mph (yes, 90mph), largely as a result of these perturbation pressure gradients.
It should be noted that there is a little feedback cycle here. Remember what you know about hodographs and storm-relative helicity. For a cyclonically-curved hodograph, a storm motion to the right wil often enhance SRH. So, a supercell turns right, and ingests higher SRH air. With this ingestion, rotation can become more intense, so the perturbation pressure gradients can become larger as well, leading to further deviation form the mean flow. Of course, there are physically limitation to this.
