Solvent extraction is a method to separate compounds based on their relative solubilities in two different immiscible liquids, usually water and an organic solvent.
You can fine more details about solvent extraction and use of a separating funnel here.
This technique is used for isolating or purifying substances by adding a second, immiscible, solvent to the original mixture. If one of the components is preferentially soluble in one of the solvents then it will migrate there and thus, when the mixture is separated again, it can be isolated.
This process is normally carried out using a separating funnel. This is a funnel with a tap, like a burette tap, on the bottom. They can be made from plastic but are most commonly made of glass.
(Image from Wikipedia)