The two fundamental sauces in garde manger work, vinaigrette and mayonnaise, are both emulsions, which can be described as uniform mixtures of two normally unmixable substances. When mixed together uniformly, using the correct technique, these substances become emulsified.
It is well known that oil and water do not readily mix, making the preparation of these sauces a challenge. Oil and vinegar are the two main ingredients in both vinaigrette and mayonnaise. Because water is the primary component of vinegar, if you combine vinegar and oil in a container they form separate layers, with the watery vinegar on the bottom and the oil on the top. If you mix them together simply by stirring, they will quickly separate and settle into their original two layers. The challenge is to get the two liquids to stay mixed. Much of the explanation of how to make these sauces is focused on this challenge.