Final answer:
The tough outer membrane that encases the brain and spinal cord is called the dura mater, which serves as a protective layer for the CNS.
Step-by-step explanation:
The tough outer membrane surrounding the brain and spinal cord is known as the dura mater. This thick, fibrous layer is the most external of the three meningeal layers and serves as a strong protective sheath, covering the entire central nervous system (CNS). It is directly anchored to the inner surface of the skull, or cranium, and extends down to the very end of the vertebral cavity. The dura mater not only protects the brain and spinal cord but also encloses the major blood vessels that enter the skull and houses vein-like structures, which are responsible for carrying deoxygenated blood away from the brain back to the heart.