Final answer:
The organelle described as the cell's "post office" is the Golgi apparatus, which modifies, sorts, tags, and ships cellular products.
Step-by-step explanation:
The organelle that acts as the cell's "post office," receiving, sorting, tagging, and shipping products like proteins and repackaging them for transportation to their final destinations both inside or outside the cell, is the Golgi apparatus. Found near the nucleus, the Golgi apparatus modifies proteins delivered from the rough endoplasmic reticulum (RER), tags them with "shipping addresses," and packages them into vesicles. These vesicles can then either fuse with the cell membrane to secrete proteins outside the cell or deliver them to various destinations within the cell. The Golgi apparatus is essential in the cell's endomembrane system, functioning alongside other organelles like the RER and lysosomes to maintain cellular operations such as protein synthesis, modification, and transport.