What is the cleaning action of soaps?

The cleaning action of soap is based on the following principle:

(1) Soap dissolves in water to form soap micelles.

(2) In water, a sodium soap dissolves to form sodium cations and soap anions. The soap anions have a hydrophobic hydrocarbon chain which is soluble in grease and oil. The hydrophilic end remains separated in water by the action of ion repulsion.