Benzoic acid is not soluble in water, despite the fact that it often dissolves in bases such as oil, grease and other organic compounds. This is because even though a base is primarily made from water, it also contains other compounds such as ether or solvated hydroxide, that soon get to work deprotonating the acid on contact.
An acid base extraction is a particularly popular exercise in educational chemistry because it allows students to separate a mixture of organic compounds and characterize them from their melting points afterwards.
Most neutral organic compounds are not soluble in water, but this is not the case when they are mixed with certain immiscible organic chemicals or liquids.
An acid base extraction involves separating compounds by converting one component from a mixture into an ionic compound that quickly renders it soluble.
Benzoic acid dissolves easily in ether or a sodium hydroxide solution, but not in regular water thanks to the deprotonating process outlined above.
The reason that deprotonating easily occurs in a base that is predominantly water is because the additional compounds often contained in a base liquid cause the benzoic acid to create sodium benzoate after deprotonation occurs. The benzoic acid quickly vanishes into the aqueous layer at this time because it has effectively transformed into a salt, which is perfectly capable of dissolving in water.