Osmosis is the diffusion of water molecules, from a region of higher concentration to a region of lower concentration, through a partially permeable membrane. A dilute solution contains a high concentration of water molecules, while a concentrated solution contains a low concentration of water molecules.
Partially permeable membranes are also called selectively permeable membranes or semi-permeable membranes. They let some substances pass through them, but not others.
The slideshow shows an example of osmosis:
In the slideshow, eventually the level on the more concentrated side of the membrane rises, while the one on the less concentrated side falls.
When the concentration is the same on both sides of the membrane, the movement of water molecules will be the same in both directions. At this point, the net exchange of water is zero and there is no further change in the liquid levels.