I THINK I understand what you're asking...so here goes:
When you have benzoic acid in diethyl ether...it is exactly that...benzoic acid...i.e. C6CH5COOH. This is soluble in ether. Yes this molecule is polar to a small extent, but not enough to make it precipitate from the liquid.
When you add NaOH solution, and shake vigorously (to ensure a fair equilibrium), then the NaOH deprotonates the benzoic acid, and leaves you with a benzoate ion...this is C6H5COO-. This negatively charge ions is VERY polar, and is virtually insoluble in the ether. It is however VERy miscible in the aqueous NaOH solution.
This allows the separation of benzoic acid from the ether...and adding strong acid to the queous NaOH will reprotonate the benzoate ion, reforming benzoic acid (which is not very soluble in water, and so it precipitates out)