Here's a breakdown:

* Nucleolus: This is a specialized region within the nucleus of eukaryotic cells. It's not membrane-bound, but rather a dense region where ribosomal RNA (rRNA) is transcribed and assembled with ribosomal proteins.

* rRNA: This type of RNA is essential for the structure and function of ribosomes.

* Ribosomal proteins: These are proteins that associate with rRNA to form the functional ribosomal subunits.

The process:

1. rRNA is synthesized in the nucleolus.

2. Ribosomal proteins, synthesized in the cytoplasm, are transported into the nucleolus.

3. rRNA and ribosomal proteins assemble together to form the two ribosomal subunits: the small subunit (40S in eukaryotes, 30S in prokaryotes) and the large subunit (60S in eukaryotes, 50S in prokaryotes).

4. These subunits are then exported from the nucleus into the cytoplasm, where they join together to form a functional ribosome ready for protein synthesis.

So, while the complete ribosome functions in the cytoplasm, its subunits are "born" and assembled within the nucleolus!