Osmosis is the diffusion of water molecules across a selectively permeable membrane. There must be a concentration gradient on either side of the membrane, from high to low concentration of solvent. Inward osmosis will occur when the amount of water (solvent)outside the membrane is greater than inside. Outward osmosis will occur when there is a higher amount of water(solvent) inside the cell relative to outside and higher solute outside. This can be demonstrated with a solution that contains salt outside a cell. The water inside the cell will leave by outward osmosis, causing plasmolysis to occur. This results in the cell dehydrating and shrinking as its contents leave.
Osmosis is the specific movement of water molecules (diffusion) across a semi-permeable membrane.
Here's an animation that explains it further: