Emulsion is the mixture of two or more liquids that do not naturally mix together. A classic example of emulsion in cooking the mixture oil and vinegar to make a simple vinaigrette.

There are two types of emulsion, temporary and permanent. A simple vinaigrette, the combination of oil and vinegar, is an example of a temporary emulsion because the two liquids only briefly stay together before re-separating. On the other had, mayonnaise, the combination of oil, egg yolks, and lemon juice or vinegar is an example of a permanent emulsion. Normally, these ingredients do not mix together, but once they have been slowly whisked together, the substances will not separate. 

References:

http://culinaryarts.about.com/od/glossary/g/Emulsion.htm

http://www.finecooking.com/item/37034/how-to-make-and-fix-emulsion-sauces