So originally, diluting wasn't a vital part of making the homeopathy treatment more effective. The guy who came up with it had the idea that "like cures like", basically, what caused a symptom in a healthy person would cure that symptom in a person who already had it from some other cause. When he actually tried this shit out, though, the person he tried it on obviously developed the symptom of the thing he'd given them. He started diluting to avoid giving them the symptoms that his "cure" would cause, and his process of diluting and then specially shaking the diluted mixture was a way of keeping it AS potent as it originally was. Eventually this turned into dilution making it MORE powerful.
Also, allopathy is the homeopathic word for "normal medicine that actually works". Other alternative medicines also sometimes use the word. They can't use phrases like "normal medicine" or "scientific medicine", because that implies that homeopathy isn't normal or scientific. They had to make up a phrase for it, because prescribing shit that actually works alongside their bullshit makes them look really good when the patient feels better.