An emulsion is a mixture of two liquids that are typically immiscible (don't blend) that forms a two phase system. One of the two liquids is dispersed in the mixture, forming the dispersed phase. The other liquid contains the dispersion and is known as the continuous phase. An example of two immiscible liquids would be water and oil. In general an emulsion will be unstable since the dispersed phase will try to decrease it's surface tension by grouping with other dispersed droplets until the liquids separate again. However, a stable emulsion can be formed by the addition of emulsifiers, such as surfactants that distribute themselves around the interface between the two liquids, creating a stable system.
Soft Matter Examples
Emulsions are an important type of "soft matter". As a system, it has many properties of a liquid but depending on the size of the dispersed phase droplets, the properties of the emulsion will be very different than those of either pure liquid.
Examples of emulsions from everyday life include ice cream and mayonnaise.