In the last 100 years the world of medicine has seen a true historical revolution. The accomplishments of modern medicine surpass the imagination, from overcoming diseases and saving lives, to organ transplants and improving the quality of life.
But modern medicine is based on the principal of "Evidence-Based Medicine" and anything that doesn't conform to this criterion is pushed aside. Thus all therapies not based on scientific proof have been expelled from the world of western medicine.
However, the public has continued using these therapies, which were given outside the formal medical system, and therefore referred to as "alternative medicine".
In the meantime, many physicians discovered that patients who received "alternative" therapies simultaneous to conventional care improved their medical condition. It wasn't always scientifically clear why this happened, but in light of these results physicians have agreed that their patients receive "alternative" care, in addition to the conventional medical care.
And thus the phrase "complementary medicine" was born: medicine that complements the trained physician's work.