Emulsification is one of the most important core principles of baking and pastry. A general definition of emulsification is the act of incorporating two or more liquids that are normally unable to mix with one another. When two liquids are incorporated in this manner it is known as an emulsion (vinaigrettes and mayonnaise are a few examples).
In baking and pastry, emulsification is almost always referring to mixing fat and water. Although fat and water will never truly bond and incorporate, by creating an emulsion the fat and water are broken down into particles that are small enough to be considered mixed for practical purposes. Emulsification is so important because it evenly disperses fat and water which is essential for proper taste, texture and leavening.