Diffusion and osmosis are important concepts for cell membranes and biological systems. Diffusion is the movement of molecules from areas of high concentration to low concentration until equilibrium is reached. Equilibrium occurs when there is no net movement of molecules. Osmosis is a type of diffusion that occurs across semi-permeable membranes, allowing certain molecules like water to pass through. Osmosis regulates water transport and turgor pressure in cells and is essential for cellular functions.