The structure that prevents water from leaving cells during osmosis is the cell membrane, specifically its phospholipid bilayer. This semi-permeable membrane regulates the movement of water and solutes into and out of the cell. While the membrane allows water molecules to pass through via special channels called aquaporins, it helps maintain the cell's internal environment. A balance of solute concentrations inside and outside the cell is essential for cell function and viability, enabling the cell to maintain its shape and functions under varying conditions.