In the culinary arts, an emulsion is a mixture of two liquids that would ordinarily not mix together, like oil and vinegar.
There are two kinds of emulsions, temporary and permanent. An example of a temporary emulsion is a simple vinaigrette. You combine the oil and vinegar in a jar, mix them up and they come together for a short time. Mayonnaise is an example of a permanent emulsion, consisting of egg yolks and oil. Egg yolks and oil would not naturally mix together, but by slowly whisking the oil into the egg yolks, the two liquids form a stable emulsion that won't separate.