Although the term adrenal fatigue is often used to describe symptoms of fatigue related to chronic stress, it is not the most accurate medical term. A preferred term is "HPA Axis Dysfunction." The HPA or 'Hypothalamus-Pituitary-Adrenal' Axis is our stress response system - when we are exposed to a stressor, either physical or psychological, our brain sends messengers down to the adrenal glands to release our stress hormones, i.e. cortisol.
While our HPA axis is well equipped to handle short term stressors, we can have a harder time dealing with long-term chronic stress. Over time our normal cortisol rhythm can be thrown out of sync, and symptoms such as those described above to appear.