Micelles are formed by association of such molecules in which both lyophilic and lyophobic parts are present. Such molecules are called surface active molecules.
Example:
Hydrocarbon chain in soap, sodium stearate C17H35COONa is lyophobic or hydrophobic while -COONa is lyophilic or hydrophilic. The hydrocarbon tails are in the interior of the micelle and COO– ions on the surface. The grease stain absorbed in to the interior of the micelle which behaves like liquid hydrocarbon. As the strain is detached from the fabric, the dirt particles sticking to the strain are also removed.
The formation of micelle and action of detergent can be explained by following figures.