The role of the Golgi apparatus in cellular processes is primarily to modify, sort, and package proteins and lipids produced by the endoplasmic reticulum. This organelle processes these biomolecules for transport to their final destinations, including secretion outside the cell or delivery to lysosomes. It plays a crucial role in post-translational modifications, such as adding carbohydrates to proteins in a process called glycosylation. The Golgi apparatus is essential for ensuring that proteins and lipids are properly processed and directed, thereby maintaining cellular function and communication.