The experiment described is an osmosis experiment. Osmosis is the process of molecules (particles) in a liquid solution, gas, or gaseous solution (but not a solid, since the molecules in solid matter are not mobile enough) balancing out in terms of concentration across a (partially permeable) membrane.
Here, the Visking tubing acts as the membrane, which would in reality in nature/biology be for example a cell membrane or the surface of a lung. Water is put on one side of the Visking tubing, and a sucrose solution (sucrose being a particular type of sugar) on the other side.
Sucrose solution is hypertonic to plain water, that is, it is more concentrated/has less water than the plain water. So in the osmosis process some of the water molecules from the plain water move over (across the membrane, or Visking tubing) to the sucrose solution on the other side. Meanwhile, some of the sucrose molecules from the sucrose move over (across the membrane) to the plain water solution. So in fact the two liquids exchange some of their molecules in order that they have equal concentration of both sucrose molecules and water molecules. If there are unequal amounts of liquid on each side, the sides might not end up with the same amount of liquid that they each started with, but will have the same concentration as the other side.
For example, if there is less water in the Visking tubing than a (for example) 10% sucrose solution outside the tubing (in the beaker), the level of the water in the Visking tubing will go down and the level in the beaker up, although both will end up with the same amount of (weaker) sucrose solution.
One could also say that the plain water is hypotonic (has more water content/less concentration of sucrose) than the sucrose solution. Liquids with equal concentration are said to be isotonic.
You could imagine that you have some water (on your side of 'the membrane') and that a large friend (a T-rex?) has a lot of water on the other, but not the recommended dietary amount, and quite a few sweets. For you both to have the recommended dietary amount of water, and share the sweets according to your relative size (the T-rex is much bigger so needs more sweets right?), you would give him some water and in exchange (by 'osmosis', which is essentially 'fairness') he would give you a couple of sweets for you to eat. Everyone's a winner!