As anyone could guess, is the process of osmosis backwards. Osmosis is the passage of water through a protein membrane (like our skin, or the inside of a plant cell) to equalize the concentration of particles dissolved in the water. The protein membrane allows water to pass through, but molecules larger than water (things like minerals, salts, and bacteria) cannot. Water flows back and forth until the concentration is equal on both sides of the membrane, and an equilibrium is formed. 
Let's apply this knowledge to water purification. We want to drink water from a lake or stream, but it contains too high concentration of contaminants like salt, minerals, and bacteria, that make it undrinkable. By applying pressure to water as it passes through a membrane, the water can be forced to move away from the membrane rather than attempting to form an equilibrium like normal. This against-flow motion is where the "reverse" in "reverse osmosis" comes from. A pump works well for this process. Water is forced through the membrane, which like a super-fine particle filter, blocks an extreme majority of contaminants from coming through.
As a purification process, it has a number of advantages as well as disadvantages. In water treatment, TFC membranes can usually remove between 96 and 99% of most contaminants, including salts and minerals, dyes, particles, bacteria, and hazardous metals. Because of the way reverse osmosis works, however, you can never truly remove all of a contaminant. You may purify down to a fraction of a fraction of a percent, but the contaminant can never be truly eliminated with reverse osmosis. Treatment systems also requires a high-grade pump, because the rejection rate is primarily dependent on the pressure applied to the membrane. That being said, smaller units have smaller ratios of permeate (clean, purified product) to waste water. This makes media filtration or other conventional filtration more effective in smaller scales (like residential settings).

what is reverse osmosis? image shows RO wiro pipe

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