Extraction is the process of selectively removing a compound of interest from a mixture using a solvent. For an extraction to be successful the compound must be more soluble in the solvent than in the mixture. Additionally, the solvent and mixture must be immiscible (not soluble in one another).
Making tea is a good example of extraction. Water is placed in contact with tea bags and the "tea" is extracted from the tea leaves into the water. This works because the "tea" is soluble in water but the leaves are not.
A Chemical Example of Extraction
A student has performed a reaction in the laboratory. When the reaction is complete she has a mixture of her product and some leftover starting material dissolved in water. If the product is nonpolar and the starting material is polar, she could extract the product into an organic solvent that is immiscible with water.
An aqueous mixture containing both product (P) and starting material (S).
An immiscible organic solvent is added and the nonpolar product is extracted into it.