This natural process called Osmosis takes place due to existence of Osmotic Pressure between two solutions separated by the Semi-permeable Membrane. The flow rate of the solvent will depend on the Osmotic Pressure, which varies with the difference in the concentration of the two solutions. The flow can be stopped or, even reversed by application of pressure on the solution in the high concentration side. This is called Reverse Osmosis and is used to produce fresh water from seawater or brackish water.
Explanation
Now consider a vessel with Semi-Permeable Membrane partition containing salt-water solution A of high concentration & solution B of low concentration or pure water at same levels. In normal conditions, the water will flow from solution B to solution A through Semi-Permeable Membrane until there is difference in levels on two sides equivalent to the Osmotic Pressure when the flow will stop.
Take a look at the adjacent diagram which pictorially depicts this scenario and the simple sketch shows two solutions in a container separated only by a semi-permeable membrane between them which performs the required task
When the level on two sides was same, flow could be stopped by application of pressure on solution A equal to the Osmotic Pressure and, the flow could be reversed by application of pressure more than the Osmotic Pressure on the solution A. This is the process of Reverse Osmosis. Higher the difference in concentration of solutions A & B, more will be the pressure required to reverse the flow.
This is the principle used for producing fresh water fro salt / brackish water. It is applied to water purification and desalination, waste water treatment, and many other chemical and biochemical laboratory and industrial processes.
References
Image of R.O. Generator from Website of FCI Water Makers