An emulsion is a stable mixture of two immiscible liquids (usually fat and water) held together by an emulsifier. Mayonnaise, hollandaise, vinaigrette — all emulsions.
The emulsifier (lecithin in egg yolk, mustard proteins) has hydrophilic and hydrophobic ends. It coats fat droplets, presenting the water-friendly side outward and preventing coalescence.
Temperature matters: heat denatures the emulsifier proteins in hollandaise, breaking the sauce. Cold fat in vinaigrette won't incorporate. Understanding the mechanism tells you why recipes fail — and how to rescue them.