What is neurobiology?
Neurobiology is the biology of the nervous system, incorporating anatomy (the structure of the nervous system, from cellular hillocks to ganglia), physiology (the function of the different areas of the nervous system), behaviour (correlating neural firing patterns to the physical reactions of a person), and molecular mechanisms and biochemistry (the nervous system in the currency of ions and molecules and how they build up larger functions).
Another term for neurobiology that is generally interchangeable with it is neuroscience, though neuroscience is a more general term and broadly integrates chemistry, physics, computing and other non-biological areas.
The relationship between neurobiology and psychology is an important one, because there is much speculation as to whether it is possible for the human mind to come from just a few pounds of grey matter. Neurobiologists attempt to build up from chemicals to cells, and from cells to nerves and the brain, and how everything works together to produce a conscious effect. There is still much speculation as to whether this is a fruitful search or not.
Neurobiology is applied in medicine as neurology, perhaps a more scientific cousin to psychiatry. Neurologists study and treat various conditions from AD/HD and Tourette's to Alzheimer's and encephalopathies.