Water alone slides right off grease. Soap is what makes the grease leave with it.
Each soap molecule has 2 ends: one that clings to water, one that clings to oil.
During a wash the oil-loving ends bury into a grease droplet while the water-loving ends face out, forming tiny balls called micelles.
Scrubbing breaks a big smear into small droplets that stay wrapped and suspended, instead of settling straight back onto the pan.
Soap never dissolves oil the way salt vanishes into water; it packages the oil so flowing water can carry it off.