The difference between potentisation and chemical dilution is significant. In potentisation bursts of energy are put into each new solution by banging it several times (succussion) with the result that the solution has a more profound effect when used to treat people. Why this should be the case is a question physicists will one day answer (rather than chemists), but the effect is observed repeatedly, and it makes it possible to use harmful substances safely.
The fact that succussion is a significant factor in preparing a remedy is less strange when it is compared with some other activities where energy is added in a discontinuous manner. For example:
The action of whipping cream is not the same as stirring it because a part and only a part of the cream is moved violently with each beat leading to a reorganisation of the material;
A pneumatic drill is much more effective because it delivers short sharp blows to a road surface, rather than continuous pressure;
An iron bar will acquire the new property of becoming a magnet by repeatedly banging it while it is in a magnetic field. 
In each of these cases controlled bursts of energy are added and they create an important change of state.
Opponents of homeopathy often argue that potentised remedies cannot have a biological effect because there is none of the original substance in the remedy. This argument is based on the assumption that chemistry is the only science relevant to biology, but research has shown that this is not the case. [2,3] Furthermore the argument assumes that the only process used when preparing a remedy is dilution, which is also not the case, since two processes are used (dilution and succussion), and it is known that banging is capable of causing significant changes. In other words the argument is unscientific because it is based on assumptions, which are not only unproven but which appear to be unprovable because they are untrue.
Often a further argument is used, that there cannot be a biological effect because there is no explanation for such an effect. This too is unscientific, since the observation of an effect must precede investigation of its cause, so effects with unknown causes are perfectly normal.
It is a curious fact that the above arguments are much more applicable to placebos, since placebos are supposed to be chemically inert and are not processed in any other way, and their action is wholly unexplained. Nonetheless opponents of homeopathy fully accept the biological effect of placebos, which is self-contradictory and unscientific.
'Potentised' or 'homeopathic' remedies?
Potentised remedies are often called homeopathic remedies because they have been prepared according to the principles of the homeopathic system, but scientifically speaking, a medicine can only be called homeopathic if it has the appropriate relationship to the patient’s symptoms. This is particularly important in the case of clinical trials of homeopathic treatment, since a treatment being tested may be described as being 'homeopathic' because of the method of preparation, when it does not actually have a homeopathic relationship to the symptoms being treated. The result of such mistakes is that the treatment does not work and homeopathy is accused of failing, whereas in fact it is the researchers who have failed to design the trial properly.
1. A F Abbott, Ordinary Level Physics, 2nd edn (London: Heinemann Educational Books, 1969), p. 376.
2. Paolo Bellavite and Andrea Signorini (trans. Anthony Steele), The Emerging Science of Homeopathy: Complexity, biodynamics, and nanopharmacology (Berkley: North Atlantic Books, 2002).
3. For a list of recent research see also 'Biological models of high dilution effects' in the uncorrected Memorandum submitted by Dr Peter Fisher HO 21 at http://www.publications.parliament.uk/pa/cm200910/cmselect/cmsctech/memo/homeopathy/ucm2102.htm.