How soap cleans?
There are substances which can be dissolved in water, as for example the salt, and others which can't, as for example oil. Water and oil don't mix together, so if we try to clean an oily stain from a cloth or from the skin, water is not enough. We need soap.
Soap is formed by molecules with a "head" which likes water (hydrophilic) and a long chain that hates it (hydrophobic).
Then when soap is added to the water, the long hydrophobic chains of its molecules join the oil particles, while the hydrophilic heads go into the water. An emulsion of oil in water is then formed, this means that the oil particles become suspended in the water and are liberated from the cloth. With the rinsing, the emulsion is taken away.
In summary, soap cleans by acting as an emulsifier. It allows oil and water to mix so that oily grime can be removed during rinsing.