The function of the nucleolus within a cell is primarily associated with the synthesis of ribosomal RNA (rRNA) and the assembly of ribosome subunits. Found within the nucleus, the nucleolus is a dense, non-membrane-bound structure that plays a critical role in protein synthesis by providing the necessary components for ribosome formation. It is responsive to cellular activity, increasing in size when ribosome production demands rise, reflecting the cell's metabolic state.