What does osmosis mean and what does the movement of water do to cells?

Osmosis can be defined as "the movement of water from an area of high water concentration to an area of low water concentration across a selectively permeable membrane". What this means, is that water tends to move from where there are lots of other water molecules surrounding it, to where there are fewer water molecules, in an attempt to even out the numbers of water molecules on either side of the membrane. The term "selectively permeable membrane" describes any membrane that allows certain molecules to move through and not others. The plasma membrane that surrounds all animal cells is a good example of this, as it allows water and some small solutes to move through it, but doesn't allow the passage of large solute molecules. 

Because of this definition then, if an animal cell is placed into solutions of different concentrations, different things happen to it. If placed into a hypertonic solution of high salt concentration (and so a low water concentration), water will move out of the cell, across the plasma membrane, down the water concentration gradient. This will cause the cell to become shrivelled, as it has lost lots of its water content. On the other hand, if you place this cell into a hypotonic solution, which has a lower salt concentration than the cell (for example, distilled water), the water molecules will move into the cell, down the water gradient, and cause the cell to swell and become lysed. 

I would demonstrate these explanations with diagrams on the whiteboard annotating the direction of water movement in each solution.