Emulsification

An emulsifier is an agent that causes fats and oils that wouldn’t otherwise dissolve in a cleaning solution to break down into small enough particles that they become suspended in the solution. Detergents contain emulsifiers that separate and suspend oil and fat in the cleaning solution until the resulting emulsion can be rinsed away, taking the dirt and oil along with it. This common process is used in cleaning dishes, clothes, and many household surfaces, which is why rinsing is important in this cleaning process.

Reference:

Don Aslett in The Cleaning Encyclopedia: Your A to Z Illustrated Guide to Cleaning Like the Pros.