Osmosis is the movement of a solvent(low concentration water) through a semipermeable membrane into a solution of higher solute concentration (high concentration water) that tends to equalize the concentrations of solute on the two sides of the membrane. (pic 1 named OSMOSIS)

The idea of Reverse Osmosis is to use the membrane as a ultra fine filter which produces clean drinking water. The water which will be purified is placed in one side of the membrane and then pressure is applied to stop and reverse the osmotic process. (pic2 named Reverse Osmosis)