Cleansing action of soap: An application of ionic micelles formation:

Let us take an example of oil or grease stick on the cloth (Fig i). When it come in contact with soap solution, the stearate ions arrange themselves around it in such a way that hydrophobic parts of the stearate ions (R) are in the oil or grease and the hydrophilic parts project outside the oil droplet. 

(http://ask.learncbse.in/uploads/db3785/original/2X/c/c4f7b8ae6a369163f36e62787cda96f3f1a2cdf2.png)

As hydrophilic part is polar, these polar groups can interact with the water molecules present around the oil droplet. As a result, the oil droplet is pulled away from the surface of the cloth into water to form ionic micelle which then washed away with the excess of water. In fact, the stearate ions of soap molecules help in making a stable emulsion of oil with water which is washed away with excess of water.