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 and-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