Homeopathy is becoming increasingly popular both for treating pets and their people. One of the things which appeals about homeopathy is that it treats the whole animal and not just the illness, as is the approach with conventional medicine. Nobody knows how homeopathy works, or even that it works at all. (At least this is yet to be scientifically proven; there is plenty of anecdotal evidence to support it). I keep a very open mind about alternative therapies and have found homeopathy effective in many cases.
Homeopathy uses remedies which are extremely dilute. The system works under the assumption that "like cures like". Therefore a substance which causes symptoms in a healthy subject similar to those caused by an illness, when given to a sick patient in very tiny amounts will cure the illness. The homeopathic system of medicine treats the whole animal not just the disease, so a nervous animal and an outgoing one would often get different homeopathic remedies for the same illness. (Using conventional medicine they would very often be given the same drug if they both had the same illness).
Conventional medicine is usually very good at treating the illness for which it has been prescribed, but it can sometimes produce unwanted side-effects. Such side-effects do not occur when using homeopathic medicines because the medicine is so dilute. (I have often heard of it being referred to as "magic water" because the active ingredient is not detectable). Conventional medicine and homeopathy can be used together with no risk of unwanted interactions between the medicines. Therefore homeopathy can be used as a complementary therapy while your animal is undergoing orthodox treatment.
Homeopathic medicines are easy to administer to pets. They come in the form of liquids, powders, or pills which generally have little taste and in the case of pills can dissolve on the tongue. It is practically impossible to overdose on homeopathic remedies and they are very cheap compared to many conventional medicines. Given the fact that there is little to lose in trying homeopathy for a given condition and that your pet can continue to receive any conventional treatment which may be necessary while on the homeopathic remedy, I would certainly consider it worth trying in any situation where the owner of an animal wished to do so.