Homeopathy

And it DOES work for many things. Beyond being a simple placebo. There is a lot of good herbal/ayurvedic medicine available in India & Bangladesh, but homeopathy is seen is much higher regard and superior in effectiveness.

It doesn't work any better than placebo, according to the only decent meta-analyses done. Sorry. But the placebo effect is actually very powerful, and very interesting. The only reason that reputable doctors refuse to take advantage of the placebos that Complementary and Alternative Medicine offers is that they don't like lying to their patients. Otherwise they could just give them sugar pills themselves, say "this will make you better" and cut out the middleman of bonkers pseudoscience.

Herbal medicine is another thing, and lots of herbs have active ingredients that affect the body. However, there's insufficient research to know whether what you're taking is safe, dangerous, or does nothing at all.

After all there's a reason for the joke "Q. What do you call alternative medicine that works? A. Medicine" Aspirin comes from willowbark and Digitalis (from foxgloves) is used to treat heart attacks. You'll notice that they give you these drugs in pills, rather than mashed up poultices. That's because the active ingredient has been isolated and studied and can now be given in a controlled dose with a predictable effect.

So does anyone have an idea of how it works? Is there some secret magic going on in the solutions?

As above: it doesn't, at least any better than sugar pills, or little bottles of flavoured water. [Unless it really does work by magic.]

Worth noticing that homeopathy has been around for about 200 years (invented by an eccentric German doctor) and no decent evidence suggesting it works, or a plausible mechanism for how it could work, have been suggested. Compare that to Quantum Mechanics, which has been around for about 100 years. Why waste time on nonsense?