The process of separation of an organic compound  from its aqueous solution by shaking with a suitable solvent is termed solvent extraction or differential extraction.
The organic compound present in aqueous layer moves to the organic solvent because:

1) the organic substance is more soluble in the organic solvent

2) organic compound being lighter moves in the upper layer

3) organic solvent is insoluble in water hence organic compound moves up

4) from the supersaturated aqueous solution the solute starts diffusing