For information on neurology and psychiatry, do a Wikipedia search for each.
http://en.wikipedia.org/wiki/Neurology
http://en.wikipedia.org/wiki/Psychiatry
I would also encourage all interested to read the following article (by Joe Martin, a neurologist and Dean of Harvard Medical School):
Martin, JB. The Integration of Neurology, Psychiatry, and Neuroscience in the 21st Century. Am J Psychiatry 159:695-704, May 2002
Basically, the reason the two fields exist as distinct entities stems almost entirely from historical reasons, rather than any rational difference. For a long time, people have artificially divided the concepts of "mind" and "body". Only in recent times have we truly begun to appreciate that the brain generates the mind and that all neurological and psychiatric disorders are ultimately biological in nature. It will be interesting to see whether the two fields merge sometime in the future.
Clinically, there are many differences, some of which were alluded to by PSYDR. In neurology, the standard clinical encounter involves a patient interview (history), followed by an exam, which tests mental status, cranial nerves, strength/coordination/reflexes, sensory systems, etc. In psychiatry, the interview comprises virtually all of the time spent with the patient and focuses almost entirely on a mental status exam that focuses on things like general appearance, mood, thought process, etc.
If you train in neurology, you will see patients with a broad array of nervous system disorders (i.e. Alzheimer disease, Parkinson disease, stroke, multiple sclerosis, ALS, Huntington disease, epilepsy, peripheral neuropathy, neuromuscular disorders, tumors, etc).
Psychiatry focuses more on "mental" illnesses/behavioral disorders such as major depression, schizophrenia, bipolar disorder, attention deficit disorder, personality disorders, etc.
There is considerable overlap, however, and both neurologists and psychiatrists may see patients with dementia (i.e. Alzheimer disease), Huntington disease, Tourette syndrome and others. In fact, in each residency training program, you will do some of the other field, though in limited amount. There are actually some neuropsychiatry training programs, in which you get board certified in both neurology and psychiatry.
As others have alluded, the line between the fields is becoming increasingly blurred (a line that was not present originally and artificially drawn in!). There are many neurologists and psychiatrists that are also cognitive neuroscientists. For your scientific interests, which clinical field you choose does not matter so much, unless you focus your research on specific patient populations that tend to aggregate to one field.
My advice would be to attend a medical school MD/PhD program that will let you do a PhD in cognitive neuroscience. From doing 3rd year clinical clerkships in neurology and psychiatry (and 4th year electives) you will see which field you like better.
Good luck!
