Emulsification is the dispersion of one phase into another in fine particals. The emulsification of fats into a dispersion allows high surface area for the fatty particles and increases the rate of any chemical reaction. One familiar emulsion is milk in which finely-divided fat particles are dispersed in water containing proteins. Hydrolysis means a reaction of a substance with water. Thus the reaction of fats with water is called hydrolysis of the fat.
Enzymes are catalysts.
Catalysts, you recall, reduce the activation energy for a process, lowering the temperature at which it can take place. You cannot hydrolyze a fat in water at any appreciable rate. The molecule is stable. Yet in the body, hydrolysis takes place quickly under the influence of an enzyme. When they mix with our food they combine with a polypeptide, colipase that helps reduce the surface tension at the oil-water interface and helps assist the hydrolysis process.