Yeah, basic principles of osmosis there, but let me see if I can make it clear. For illustration's sake, I'll take glucose as a solute and water as a solvent, but recall that the principles are true (though they can have added complexity) for other solutes and solvents (see this post on chem.SE).
The basic principle behind osmosis is that conjoined systems tend toward equal concentrations. In other words, if you have a more concentrated solution (more particles of glucose per amount of water) on one side of a membrane than the other, the solution "wants" to become equal on both sides of the membrane.
If the membrane is permeable, there's no problem: glucose can flow freely and equilibrate on both sides of the membrane. So the solution just moves around "mixing" until there's the same concentration everywhere of solutes (ie., glucose) in the solvent (ie., water).
On the other hand, suppose that the membrane is semi-permeable, meaning that the the water can pass through but the glucose cannot. The system still "wants" to get to equilibrium; a state of equal concentrations on either side of the membrane, but it cannot get the solute across. What happens instead is that water starts moving from the side which is less concentrated to the side which is more concentrated. This results in the concentration of particles on less concentrated side going up and the concentration on the more concentrated side going down, effectively equilibrating them.
Now look at Picture 1. Intuition from all this would tell you that the concentrations would be equal. However, there's a twist. Osmosis can only exert so much pressure on a system, and if it has to resist a pressure, it eventually stops, even if the concentrations are not equal.
The assumption in the picture is that the balloons have the same elasticity, meaning that the balloon on the left is more stretched, and is exerting more pressure on the solution than the balloon on the right. Therefore, it will counteract some of the osmotic pressure and push some water back onto the right side of the system.
Now look at Picture 2. Again, intuition would tell you that the balloons will have equal concentrations at the end of the scenario, but again, the pressure that the balloon on the left is exerting messes things up a bit. Even though the balloon on the right is pushing water into the balloon on the left, it is unable to push as much as it would like to, because the pressure of the left balloon's elasticity counteracts the osmotic pressure.
Taking it to the next level
They're basically laying the foundation work for reverse osmosis in this question. In the case of reverse osmosis, we would be artificially applying pressure to the balloon on the left, resulting in water flowing forcibly into the right container. This can be an advantage if you want to increase the concentration of a liquid - which has hundreds of industrial usages, such as in concentrating maple syrup in Canada and the northern States.