What is the function of the rough endoplasmic reticulum?

The rough endoplasmic reticulum is a membranous structure that associates closely with the nucleus. Embedded in the membrane of the structure are ribosomes, this is what gives the "rough" appearance. RNA passes through the ribosomes where its sequence of nucleic acid codes for specific amino acids to be joined up in a specific order. The route through the ribosomes for the amino acid takes them into the membranes of the reticulum where they can be kept together. They are then moved of in vesicles formed from the ER membranes to the Golgi Apparatus to be packaged and processed.

The rough ER is involved in protein synthesis. There are ribosomes attached to the surface, giving it a bumpy or 'rough' appearance. Ribosomes are the site of protein synthesis.

It transports material through the Cell and produces proteins in sacks called cistren or cisternae which are sent to the Golgi body for export, or for insertion into the Cell membrane.
The rough endoplasmic reticula synthesize proteins. For more detailed information - see the related link to Wikipedia.