Water is a polar molecule, and grease is non-polar. Polar sticks to polar and non-polar to non-polar. Soap has both polar and non-polar ends, so it will dissolve in both water and grease to form a more free-flowing mixture.
Soap molecules are hydrophobic at one end at they are attracted to the other end. The hydrophobic portion of the soap molecules mixes with oil while the hydrophilic portion of the soap molecule mixes with water. Learn more from http://www.elmhurst.edu/~chm/vchembook/554soap.html.