Solubility Demonstration I -- Like Dissolves Like
Chemical Concept Demonstrated
The iodine crystals dissolve in the lower layer, while the potassium permanganate crystals dissolve in the upper layer.
Iodine and carbon tetrachloride are both nonpolar, so the liquid dissolves the solid. The water layer does not dissolve the iodine because water is polar.
A similar explanation can be used to show why the permanganate dissolves in the water and not the tetrachloride, but it should be sufficient to say that "like dissolves like."
The same principles of polarity also explain why the water and carbon tetrachloride don't mix in the first place.