A dish-soap molecule is amphiphilic: a polar, water-loving hydrophilic head attached to a long non-polar, oil-loving hydrophobic tail. That split personality is what makes soap work — and it's exactly what the small dumbbell-shaped particles in this scene represent (blue head, orange tail).

Lowering surface tension

Dumped into water, surfactant molecules crowd the air-water and oil-water interfaces, tails pointing away from the water. This disrupts the hydrogen-bond network at the surface and drags the surface tension down from about 72 mN/m for pure water toward roughly 28-30 mN/m for a typical dish-soap solution.

The critical micelle concentration

Below a threshold concentration — the critical micelle concentration (CMC) — added surfactant keeps packing onto interfaces and surface tension keeps falling. Past the CMC the interfaces are saturated, so new molecules instead self-assemble in the bulk water into micelles: spherical clusters with tails huddled inward, away from water, and heads facing outward. Surface tension flattens out, but the population of micelles keeps growing — and micelles are the workhorses that actually solubilise grease.

Emulsification

At a grease patch, surfactant tails burrow into the oil while heads stay in the water. Enough of them ringing a patch peel a droplet free and wrap it completely, tails in, heads out: a grease droplet now disguised as something water-soluble. This is emulsification — the grease hasn't dissolved, it's been encapsulated and suspended, so it rinses away instead of redepositing on the plate.

Why hot water and scrubbing help

Grease is a waxy solid-to-viscous-liquid at room temperature. Hot water lowers its viscosity, so surfactant tails penetrate it faster and freed droplets float off more easily. Scrubbing is mechanical agitation: it thins the stagnant boundary layer at the oil-water interface and physically shears grease into smaller fragments, both of which speed up the mass transfer of surfactant to the interface and grease into the water.