The distilled water is hypotonic to the cells of the potato because it has a lower solute concentration. As a result, water will flow into the cells of the potato by osmosis and they will swell and burst. Thus the potato will become squishy. Osmosis is just the movement of water across a semi-permeable membrane. The 0.3M solution is isotonic to the potato - they have the same solute concentration. Nothing will happen when the potato is placed in this solution. The 0.6M solution is hypertonic to the solution in the cells of the potato and thus water will leave the potato and flow into this solution. As a result, the potato will shrivel up and look dried up. This is called crenation.