Why does soap clean?

What is happening?

Soap and many detergents are surfactants. Their molecules contain a water-compatible head and a hydrophobic tail. At interfaces they can lower surface tension and change how water wets a surface.

Around oily dirt, surfactant molecules can arrange so that their hydrophobic parts associate with the oil while the water-compatible parts face outward. This helps disperse grease into the wash water.

What changes it?

Mechanical action and rinsing still matter. Soap does not make dirt vanish: it changes the interfaces so oily material can detach, remain dispersed and be carried away.