Forward osmosis- in which two liquids of varying concentration are separated by a permeable membrane. The fluid of lighter concentration tend to move towards the concentrated fluid through the membrane. This is a natural process. Example - suppose, if you spend lots of time swimming in the sea water, the water in your body (lighter compared to sea water) tend to move out towards the sea water, effectively using your skin as a membrane.
Reverse Osmosis is just the opposite. The high concentration liquid is forced on to the lighter concentration side by mechanical pressure. Example - water purification systems. When salt water or mineral rich water is forced through a membrane, the membrane is effectively trapping the unwanted salt and minerals, leaving us pure water to consume. Depending upon the type of membrane used, more/less minerals can be trapped.