Osmosis is a natural phenomenon where the water molecules will seep through the semipermeable membrane separating 2 compartments, from an area of lower concentration to the area of higher concentration until equilibrium is achieved. This occurs as a result of Osmotic pressure.
Reverse osmosis on the other hand is required to overcome the natural osmotic pressure and hence additional mechanical pressure is applied on the side of high concentrated solution so that the direction of flow of water reverses and hence leaves behind the salts obtaining pure water on the other side of the membrane. This is widely used for the desalination process of sea water.