Benzoyl Peroxide is very effective against acne. It destroys Propionibacterium acnes - a bacteria that causes this problem. That's why it works so great. It also helps to renew and exfoliate dead cells helping to make the skin cleaner. You can find this component in many anti-acne products.
BUT you should avoid this component if you have dry skin. Even people with oily skin notice that it dries the skin hard. Be careful!
Water is a great solvent. It’s neutral and doesn’t provide any strong positive or negative effects. It just helps components to mix better and to transport active components.
Cocamidopropyl Betaine is a pH 4.5-5.5 liquid that is used to improve the overall efficiency of the formulation. It’s usually combined with different surfactants and is used because of its cleansing efficiency. It helps to remove sebum and dirt from the skin and hair. It also works as a foaming agent helping to make a pleasant foam.