The word "release" is an euphemism (a nice way to describe something that's unpleasant) for death. Basically, those who are found wanting in any way are "released," or killed.
In the world of The Giver, "release" is granted when a newchild or a twin sibling fails to thrive, when an elderly member of the community has outlived his years (and is ready to die), when someone commits an unforgivable offense three or more times, or when someone requests it. The only member of the community who cannot ask for release is the Receiver.
No one gets to witness a release; most people in the community believe that release is a positive experience, a means of transcending the human existence. So, when Jonas is invited by the Giver to witness a release, he is devastated by its brutal reality. You can read about Jonas's traumatic experience in Chapter 19.