What specifically happens in your body/mind to cause a throbbing headache?

Dehydration. If you don't drink enough water the brain shrinks slightly which causes strain on the bits that anchor your brain to your skull (pulling them tighter than normal), which causes the headache.

With the exception of migraine headaches, which are a different type of headache, headaches are simply painful symptoms of an underlying systemic problem or cause.
No specific cause can be fingered as the culprit responsible for the end result of a painful headache.
A multitude of causes exist for a headache, each of which has a different trigger mechanism, but the resulting headache in all cases is a red flag signaling a disorder somewhere in the body or in the nervous system.
In most cases, the anatomy of a headache can be dissected and understood, once it is traced back to its physical or neurological origin. The actual pain we experience does not stem from the actual brain matter contained in the skull, but from the pain felt by the sensitive coverings of the brain, and of the large veins and arteries which drain fluid from the brain. Sinus, tooth, ear, and muscle pain produce headaches by radiating the pain to these sensitive coverings when they tense, and when the muscles spanning the neck and the base of the skull contract.
Complaints of headaches commonly fall under the heading of vascular headaches, and result when the arteries in the skull dilate, often because of triggers that include hunger, caffeine deprivation, and hangovers. Other cases simple to diagnose include cases where people experience the effects of sudden physical and emotional trauma from an automobile accident. The violent jolts their bodies sustain, or the effects of their necks twisting, often result in headaches, because the trauma from pulled or tensed muscles triggers pain in the sensitive brain structures.
Further, severe emotional trauma causes muscles over the back and at the lower part of the head and the neck to contract, resulting in an instantaneous headache.
The important thing to remember, when one experiences a headache, is that it is a symptom of underlying disorders, with multiple causes, that should command respect, and that merit diagnosis.

http://neurology.health-cares.net/headache-causes.php

http://www.healthsquare.com/headaches4.htm

http://www.headaches.realage.com/content.aspx/topic/26

http://www.medicinenet.com/headache/article.htm