The structure in plant cells that stores materials and maintains cell rigidity is the vacuole. Vacuoles are large, membrane-bound organelles that store various substances, including water, ions, nutrients, and waste products. In many plant cells, the central vacuole also helps maintain turgor pressure, which is essential for keeping the plant upright and healthy. Additionally, vacuoles play roles in cell growth, metabolism, and the overall physiological balance of the cell.