The relative solubilities of each compound are different in the other one.
"Partially miscible" means that the liquids do not mix entirely or evenly. Instead of a homogeneous 50:50 mix each layer will have a different composition.
One way to think of it is as the relative solubility of one fluid in the other. The primarily water fraction could be seen has having a solubility of up to 5% phenol. Then, the phenol layer can be seen as having a solubility of 30% water.