Euphemisms use "a mild, indirect, or vague term for one considered harsh, blunt, or offensive." As such, euphemisms may be used to hide what is actually being done or to disguise the impact of some action.
Elderly residents in the community live in the House of the Old (which our culture might call a nursing home) that has as a main area the Releasing Room. This is the place in which the old are "released", a process that we would call either murder or suicide. Describing the death of a person as a "release" is using a euphemism.
During the story, Jonas experiences dreams that his parents recognize as the beginning of the "stirrings," which are controlled by daily pills taken from the time the stirrings begin until one enters the House of the Old. The "stirrings" are sexual feelings and desires.