"Something" damages brain cells and causes them to die. The brain in Alzheimer's actually shrinks in volume as shown on a MRI. As far as I am aware, they still do not know for sure what causes it for certain and there are different theories. There quite possibly could be multiple different causes and several different flavors of Alzheimer's.

One theory I subscribe to is that the brain cells no longer utilize glucose properly and actually are starving and dying. One support of this theory is that when people are put on a strict ketogenic diet or given supplemental exogenous ketones, supplying the brain with an energy source supplemental to glucose, symptoms improve. Not a cure, because the damage done cannot be repaired quickly (brain cells are a very long life low turnover cell in the body compared to fast turnover cells like red blood cells, when they die it takes a long time for the body to replace them. A time line an already old person does not have). But ketones show improvement of current symptoms and slowing of the degradation of quality of life. It gives hope that maybe some day the cause will be determined with certainty and prevention can be the main treatment. Once a person is diagnosed about the best that can currently be done is hopefully slow the decline. Medicines available to treat it have mostly been a dismal failure.