This is called osmosis (movement of water down its concentration gradient). Initially, there is no net movement of water from the left to the right compartment of the beaker. If the right compartment of the beaker contains solutes that cannot penetrate the semipermeable membrane, osmotic pressure forces water to enter the right compartment from the left compartment, increasing the height of fluid in the right compartment until the difference of hydrostatic pressure is equal to the difference of the osmotic pressure, at which point the pressure equalizes.
When hydrostatic pressure is produced by osmosis, it results in a pressure gradient across the membrane. This net imbalance on either side of the beaker causes a rise in the level of the solution. This rise of solution continues until the hydrostatic pressure of the solution in the right compartment is sufficient to force water molecules back into the left compartment.