During the cleaning action of soap --- part of soap dissolves in the dirt and encapsulates to form micelle

soap is sodium stearate, C17H35COO- Na +     C17H35  group is the hydrophobic part,-COO-  is the hydrophilic part.  dirt and grease particles are non-polar.The non-polar hydrophobic part C17H35  group dissolves in greasy droplets     Thus the hydrophobic part of stearate ions is in the oil droplets and hydrophilic projects out of the grease droplet like bristles