Most soaps have in them a great deal of something we call alkali. This alkali simply dissolves the oil that gathers on things, and so it makes them clean. But soap takes away the dirt from things in another way, as we know when we use soaps that have no alkali in them at all. It has the power of breaking up oil into number of very tiny little drops, which are easily washed away, together with all the dirt that the oil has caught and collected.
A collection of very tiny drops of oil, held in some other fluid, is called an emulsion. Water alone will not form an emulsion of any oil, because oil and water will not mix. That is the reason why we cannot wash well with water alone. But when water has soap dissolved or melted in it, it is able to make an emulsion of the oil on anything we are washing, and so makes it clean.