Nadine Cabot suffered a ruptured aneurysm, which caused a cerebral hemorrhage. This is properly called a cerebrovascular accident, or a hemorrhagic stroke (the other sort of stroke is called ischemic, and occurs when a clot or other foreign body blocks a blood vessel). Blood irritates neurons (brain cells), which causes them to swell. The damaged artery does not conduct blood where it needs to go properly, further imperiling cells by depriving them of oxygen. These hazards can, if severe enough, kill regions of the brain, resulting in deficits. If the damage is not too severe and the patient works hard to rehabilitate, some or all of the loss can be recovered as the brain, a remarkably plastic organ, can recruit new neurons to do the jobs of the destroyed cells, rewiring itself in essence. It is not known why certain people develop what are called berry aneurysms (their names comes from their general shape). Genetics probably plays a role. Uncontrolled hypertension is a risk factor, as is diabetes, especially if refractory or poorly controlled.
Cerebral angiography involves routing a catheter through the arteries and into the brain. A contrast agent is injected via this catheter and X-ray images made. The contrast agent is designed to show up well on an X-ray, enabling doctors to see the basic structure of the cerebral vasculature. With this information, they can identify the source of the problem and plan their surgical intervention properly. Sometimes, they can correct an aneurysm without surgery, by inserting a coil of platinum wire through the catheter; this coil promotes the growth of connective tissue which patches the defect. (This procedure did not exist at the time this show was produced.) In a modern clinical setting doctors would probably use computer-aided tomography - a CAT scan - to identify the problem first, since this procedure is much less invasive.