It's the placebo effect. People want to feel better, so they trick themselves into feeling that they are better.
Homeopathy makes no chemical sense. If you know anything about chemistry, then you'd know that homeopathy is literally impossible. The "less" there is of something, the "stronger" the effect? Nothing else works that way at all! Less poison doesn't kill people faster. Less detergent doesn't get plates cleaner.
Now, homeopaths claim that they don't need active ingredients, because the water forms a "memory" of the diluted material and enhances the effect. Again, to anyone who even stayed awake through PRIMARY school science classes, this is NONSENSE. What is forming the memory? How is the "memory" stored in the water? Not one of them has proved that water can form a memory (at least not to any respectable standard of proof).
The only people who could believe in Homeopathy are those who know nothing about science. To anyone who believes in Homeopathy: Pick up a chemistry textbook and read it. Go to the public library, get a textbook on Chemistry and read the first 3 chapters.
Chemistry and Homeopathy are incompatible. One has given us all the modern chemicals and plastics and reagents and has helped create the technology around you today. The other has nonsense combined with vague sciency-sounding words and bottles of mostly (if not entirely) water masquerading as medicine.