Reverse osmosis systems remove almost every contaminant you could possibly have in your water. But they also filter out "good" minerals such as fluoride. The process wastes water... potentially up to five gallons of water for every gallon of purified water produced, and it flushes contaminants back into the water supply. Therefore, reverse osmosis should be considered only if there are specific contamination problems.

Reverse osmosis (RO) is a separation process that uses pressure to force a solution through a membrane that retains the solute on one side and allows the pure solvent to pass to the other side. More formally, it is the process of forcing a solvent from a region of high solute concentration through a membrane to a region of low solute concentration by applying a pressure in excess of the osmotic pressure. This is the reverse of the normal osmosis process, which is the natural movement of solvent from an area of low solute concentration, through a membrane, to an area of high solute concentration when no external pressure is applied. The membrane here is semipermeable, meaning it allows the passage of solvent but not of solute.

The membranes used for reverse osmosis have a dense barrier layer in the polymer matrix where most separation occurs. In most cases the membrane is designed to allow only water to pass through this dense layer while preventing the passage of solutes (such as salt ions). This process requires that a high pressure be exerted on the high concentration side of the membrane.

Sources:
http://www.consumersearch.com/www/kitchen/water-filters/
http://en.wikipedia.org/wiki/Reverse_osmosis#Drinking_water_purification