Brain waves occur at various frequencies, that is, some are quick, some quite slow.
Thus the presence of alpha can show the presence of an awake, resting state. If it is present at a fairly high voltage when the eyes are open, this would usually indicate an inattentive, daydreamy state. In fact we often see this sign in adolescents and adults with attentional difficulties. The beta family of waves happen at frequencies from 16-40 Hz or higher. Delta and theta waves are relatively slow.