What difference does rooting hormone make when propagating plants from cuttings? I have have been successful with and without it, but I would like to know for example, if it affects the speed or health of the growth.
There is a very full description of the various types of hormone rooting compound here.
As already pointed out, it is supposed to stimulate root formation; I have tried using it on cuttings a couple of times, but haven't fond it effective; in fact, if anything, some of the cuttings would probably have done better without it.
According to the New Encyclopedia of Gardening Techniques (Royal Horticultural Society):
It is meant to stimulate root growth - in particular to stimulate the creation of roots.
I've only tried it on peach cuttings so far, and haven't don't a comparison with/without. These had mixed results but for other reasons - first time it was the wrong time of year, and the second time most of the cuttings were too immature.