Although I have tried to write this essay in a way that is accessible to the non-expert, it will still be helpful to first familiarize you with basic knowledge of the structure of the brain and the roles played by different cell types within the brain.
At the simplest level, the brain can be characterized as consisting of two major components: the gray matter and the white matter. The gray matter comprises the bodies of the neurons, including the cell nucleus, and the white matter contains the myriad of "wires" that connect each neuron to every other neuron it communicates with. The wires are known as "axons" and they can be quite long, connecting, for example, neurons in the frontal cortex (above the eyes) with other neurons deep in the interior of the brain concerned with memory and movement. The axons will figure prominently in the discussions below, because they are coated with a fatty substance called the myelin sheath, and this insulating layer is known to be defective in Alzheimer's. Neurons pick up signals transmitted through the axons at junctures known as synapses. Here the message needs to be transmitted from one neuron to another one, and various neurotransmitters such as dopamine and GABA exert excitatory or inhibitory influences on signal strength. In adidtion to a single axon, neurons typically have several much shorter nerve fibers called dendrites, whose job is to receive incoming signals from diverse sources. At a given point in time, signals received from multiple sources are integrated in the cell body and a decision is made as to whether the accumulated signal strength is above threshold, in which case the neuron responds by firing a sequence of electrical pulses, which are then transmitted through the axon to a possibly distant destination.
In addition to the neurons, the brain also contains a large number of "helper" cells called glial cells, which are concerned with the care and feeding of neurons. Three principle types of glial cells will play a role in our later discussion: the microglia, the astrocytes, and the oligodendrocytes. Microglia are the equivalent of white blood cells in the rest of the body. They are concerned with fighting off infective agents such as bacteria and viruses, and they also monitor neuron health, making life-and-death decisions: programming a particular neuron for apoptosis (intentional self-destruction) if it appears to be malfunctioning beyond hope of recovery, or is infected with an organism that is too dangerous to let flourish.
The astrocytes figure very prominently in our story below. They nestle up against the neurons and are responsible for assuring an adequate supply of nutrients. Studies on neuron cultures from rodent central nervous systems have shown that neurons depend upon astrocytes for their supply of cholesterol . Neurons critically need cholesterol, both in the synapse  and in the myelin sheath , in order to successfully transmit their signals, and also as a first line of defense against invasive microbes. Cholesterol is so important to the brain that astrocytes are able to synthesize it from basic ingredients, a skill not found in most cell types. They also supply the neurons with fatty acids, and they are able to take in short chain fatty acids and combine them to form the longer-chain types of fatty acids that are especially prominent in the brain , and then deliver them to neighboring neurons and to the cerebrospinal fluid.
The third type of glial cell is the oligodendrocyte. These cells specialize in making sure the myelin sheath is healthy. Oligodentrocytes synthesize a special sulfur-containing fatty acid, known as sulfatide, from other fatty acids supplied to them by the cerebrospinal fluid . Sulfatide has been shown to be essential for the maintenance of the myelin sheath. Children born with a defect in the ability to metabolize sulfatide suffer from progressive demyelination, and rapid loss of motor and cognitive functions, resulting in an early death before the age of 5 . Depletion in sulfatide is a well-known characterization of Alzheimer's, even in early stages before it has been manifested as cognitive decline . And ApoE has been shown to play a crucial role in the maintenance of sulfatide . Throughout a person's life, the myelin sheath has to be constantly maintained and repaired. This is something that researchers are only beginning to appreciate, but two related properties of Alzheimer's are poor quality myelin sheath alongside a drastically reduced concentration of fatty acids and cholesterol in the cerebrospinal fluid .