What are cranial nerve nuclei?
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.