The term for the structure in cells that processes and packages proteins is the Golgi apparatus. It is involved in modifying, sorting, and packaging proteins that are synthesized in the endoplasmic reticulum (ER) before they are sent to their final destinations. The Golgi apparatus consists of a series of stacked membrane-bound sacs called cisternae. It plays a crucial role in ensuring that proteins are properly folded and functional, and it is responsible for the addition of carbohydrates to proteins, making them glycoproteins. This process is essential for the secretion and transport of proteins within and outside of the cell.