As letmetellu said, "Water has a surface tension and the soap will break this tension".
Actually, it doesn't "break" the surface tension, it lowers it. A lower surface tension helps the wetting process. Soaps have one hydrophobic (water hating) end and one hydrophilic (water loving) end. The hydrophobic end gets into the grease and the hydrophilic end gets into the water. The result is that the grease is effectively hidden from the water and vice-versa. You get an emulsion of grease (oils) and water.
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