Most liquids will dissolve into one another.
Some, however, won’t. They have to be encouraged to bind together. This encouragement process is referred to as “emulsifying” and the result can be called as “emulsification.”
The process involves dispersing very teeny droplets that can be measured in microns of one liquid through the other. Emulsions are unstable, though, always ready to return to their natural states.
Added ingredients that make emulsions more stable are molecules of stuff like lecithin (either used by itself as an extracted ingredient, or being provided naturally by tossing in an egg yolk.) One end of a lecithin molecule attracts water, the other half repels it. Consquently, a lecithin molecule ends up with one end attached to water, the other to something such as a fat. In this way, it acts as a mini bandage holding the two disparate elements together.
The process is particularly applied to the combination of liquid fat and another liquid, with vinegar and oil being the classic two usually referred to.
Other foods that are emulsifications, whether we realize it or not, are butter, Hollandaise Sauce, margarine and mayonnaise.