This video explains why soap is used to remove oil and grease.
We know that oil and water do not mix. So, water alone cannot remove oil stains. In this video we see that even after the 2 liquids are mixed together vigorously in a test tube they separate, with the oil lying above the water. However, when in addition to water and oil, some liquid soap is added and the mixture is vigorously shaken, the separation of oil and water is not seen. This is because soap has both hydrophilic and hydrophobic ends. The hydrophilic end combines with water and the hydrophobic end with the oil allowing the formation of an emulsion. This property of soap allows oil to combine with it and so soapy water can remove oil stains.