I am having a really hard time trying to understand what cranial nerve nuclei are. I have been reading/watching videos and I keep hearing, "that is where the cranial nerves make connection with the brainstem." Also, I keep hearing that some cranial nerves may have multiple nuclei and some nuclei may have multiple nerve synapsing there; however, this information doesn't really help me understand what they are. Are they a processing center? If so, doesn't information get processed in the cortex? So the main question is: What is a cranial nerve nucleus and what is it's function? What does it mean by "where nerves make connections"? I am attaching the image which I've been studying. You may refer to that when answering this question.
Nerves (including cranial nerves) are constituted of neurons, and other supporting cells and structures (e.g. myelin sheath and extracellular protein matrix). Neurons are highly specialized cells that have a particular cellular anatomy:
As you can see, the cell body (or soma) contains the nucleus, and projects it's axon towards other structures in the body, sometimes more than a meter away! Cranial nerves (like other nerves) are a collection of the axons, not the cell bodies themselves. The cell bodies reside together, in the brainstem, forming what we call nuclei. So that's simply what they are.