Emulsifying is a very old cooking technique. Basically, it is when two liquids that don't mix become combined in a way that is stable. The tendency to separate and break apart remains but an added emulsifying agent can help stabilize or strengthen the colloid by binding the liquids together.
The majority of culinary emulsions are water based. These emulsions can take one of two forms, either water-in-oil, where the water is dispersed in the oil, or oil-in-water, where the oil is dispersed in the water. Some common oil-in-water emulsions are mayonnaise, Hollandaise sauce, vinaigrettes, and milk. Butter is the most common example of a culinary water-in-oil emulsion.
Movement is an important part of the process for many emulsions since it is what disperses the molecules into the base substance. Often times a whisk or wooden spoon is needed for this process.
From the moment the whisk or wooden spoon makes contact with the ingredients, the substances begin to break down into smaller particles. The more movement there is the smaller the particles become, making the emulsion stronger.
You can read more information about emulsifying from my guide on how to emulsifying or from the emulsifying articles below.