Osmosis is the passing of a less concentrated solution into a high concentrated solution through a membrane, creating a closer equilibrium between the two.
A Reverse Osmosis (R.O.) unit creates a purer solution (less concentrated) from a pressurised source (usually mains water) by forcing the water through a semi permeable membrane, allowing only almost pure water through. Most R.O. units will remove between 95-98% of all impurities in the source water.
R.O. water itself is actually too 'pure' for use with fish so the useful minerals and salts need to be reintroduced before use in the aquarium. For marine aquariums, softwater or sensitive freshwater fish, R.O. water gives the fish keeper a much better quality source of water, to which proprietary minerals can be introduced, creating tailor made conditions for the aquarium.