Osmosis is a chemical process where smaller molecules pass through a semi-permeable membrane in the direction where a higher concentration of larger molecules that cannot pass through the membrane exist. As a result, the concentration of the smaller molecules on each side of the membrane is equalized in the long run. Osmosis is very common in the body, where it accounts for much of the movement of water through the body's tissues. For example, most of the body's membranes will not allow the passage of sodium and chlorine ions, and water tends to travel in the direction of those ions. By having other tissues be permeable to those ions, the body can largely control whether or not water travels between tissues.
Edema occurs where water that normally passes into other tissues cannot do so, often because the balance of ions in the other tissue has changed (generally becoming too full of fluid themselves).