Potentization (also known as succussion) is the term homeopaths use to describe the series of stepwise dilutions used in preparing their medications. A potentization involves taking a portion of a mixture and diluting it in a volume of clean solvent, usually water in a ratio of 1:100, and then striking the container 10 times against an elastic object. They do this because, obviously, just diluting the stuff to make a medicine is just plain silly.
The whacking bit is called succussion, a term that originally meant "shaking" as used in chemistry and alchemy. Its use today is almost entirely with respect to homeopathy, although the term is occasionally used in reference to the sound of splashing fluid in a body cavity. Impressive science sounding terms are known to increase the placebo effect by making the treatment appear more complex and more effective, and this applies equally to homeopathy as all alternative (and proven) medicines. There is a strong lack of evidence to suggest that any of the proposed steps used in potentization actually do anything to the solvent at all, and so there is no discernible difference between merely "diluted" homepathic solutions and properly "potentised" ones.
 Whacking it
Shaking and agitating the mixture is an important part of the potentization process. Samuel Hahnemann believed that this was a key part of the homeopathic practice and that it would "release dynamic forces from the diluents which were preserved and intensified with subsequent dilutions". In modern homeopathy, it is this process that is said to impart water memory upon the solvent.
In Hahnemann's original work, he had a leather bound board which he used to strike the solutions against. In mass produced homeopathic remedies, the potentization is performed mechanically. What constitutes succussion, however, is poorly defined. The number of "strikes" varies wildly between 10 and 50 and the actual methodology is not consistent, varying between striking it against a board, tapping it, or shaking it. In order for the succussion process to be meaningful, it must be consistent; otherwise skeptical ideas regarding sewage imparting a memory on water still hold, as the treatment plant could easily be performing a potentiating "succussion" on the water. Modern homeopathy holds that succussion gives the water the "energy" it needs, but again, the quantity of energy is undefined as are questions about whether this energy could be supplied through other means. Bach flower remedies, for example, use sunlight as their "potentiating energy source", similar to that old recipe for a martini that involves passing a sunbeam through a bottle of vermouth.
The fact that potentization involves shaking means that many amateur skeptic views on homeopathy are actually straw man arguments. What needs to be proved is not that there is no active ingredient, which is easy and not denied by modern homeopaths, but that succussion does not impart water memory or potentate the remedy. This is easy to demonstrate, but the wide variety of succussion techniques lead to many chances to move the goal posts or potential escape hatches for homeopaths.
 Possible "explanations"
Given the above poor definitions, it is possible that succussion acts to aerate the mixture, thus changing its properties. However, if this were the case, it would be possible to tell the difference between homeopathic solutions and normal water by looking at the concentration of dissolved gases. These differences have not been observed, despite thorough testing. And even if they were, the dissolved gases would return to equilibrium. This is exactly what happens to a carbonated soft drink that goes "flat" when removed from its pressurized container and can happen on a timescale of minutes to hours. Meanwhile, homeopaths only recommend that mixtures are succussed every few weeks to keep them somehow fresh.