The primary function of the Golgi apparatus in a cell is to modify, sort, and package proteins and lipids for secretion or delivery to various cellular destinations. It acts as a processing plant, receiving proteins synthesized in the endoplasmic reticulum and refining them through enzymatic reactions. The Golgi apparatus plays a crucial role in post-translational modification, such as glycosylation, and is essential for producing secretory vesicles that transport materials outside the cell.