Why does hyperventilation reduce intracranial pressure?

Vasoconstriction: Hyperventilation causes low carbon dioxide which leads to increased blood pH level (alkalosis) which causes blood vessels to constrict. Alkalosis also causes decreased freely ionized blood calcium, which results in cell membrane instability and subsequent blood vessel constriction. Hyperventilation reduces intracranial pressure as a result of this vasoconstriction within the brain.

Reducing CO2: Carbon dioxide (co2) opens up the cerebral blood vessels and increases the volume of blood in the head, increasing intracranial pressure (icp). Hyperventilation is used acutely to reduce the co2 and therefore the icp.

Chemosensors: In the blood vessels. Think of your intracranial blood vessels as tubes that react to the concentration of various chemical products. One of them is carbon dioxide. When you breathe fast your co2 level decreases and the vessels constrict. When you hold your breath the co2 level increases and the vessels dilate.