Unlike plant cells that have rigid cell walls, animal cells have flexible cell membranes that allow the cell to enlarge or shrink. This membrane also controls what enters and leaves the cell, and when the concentration of salts and other molecules in external fluid changes, the cells reacts by changing the inner concentration to match what's outside. So if the external solution becomes more dilute, or hypotonic, water will move into the cell until it balances the internal and external concentration. As a result, the cell enlarges, or swells. Such changes can be minor or, if the change is severe, might damage or destroy the cell.
A hypertonic solution contains a high concentration of the solute compared to the solvent molecules. Which basically means, the water molecules are more inside the cell, than in the solution. So, the water molecules within the cells diffuse out and the solute molecules move in, making the cell shrink.