Cytolysis, or osmotic lysis, occurs when a cell bursts due to an osmotic imbalance that has caused excess water to move into the cell. It occurs in a hypotonic environment, where water diffuses into the cell and causes its volume to increase. If the volume of water exceeds the cell membrane's capacity then the cell will burst.
Cytolysis does not occur in plant cells because plant cells have a strong cell wall that contains the osmotic pressure, or turgor pressure, which would otherwise cause cytolysis to occur. Contrary to organisms without a cell wall, plant cells must be in a hypotonic environment in order to have this turgor pressure, which provides the cells more structural support, preventing the plant from wilting. In a hypertonic environment, plasmolysis occurs, which is nearly the complete opposite of cytolysis: Instead of expanding, the cytoplasm of the plant cell retracts from the cell wall, causing the plant to wilt.
Different cells and organisms have adapted different ways of preventing cytolysis from occurring. For example, the paramecium uses a contractile vacuole, which rapidly pumps out excessive water to prevent the build-up of water and the otherwise subsequent lysis.
Other organisms pump solutes out of their cytosol, which brings the solute concentration closer to that of their environment and slows down the process of water's diffusion into the cell, preventing cytolysis. If the cell can pump out enough solutes so that an isotonic environment can be achieved, there will be no net movement of water.