Release is death by lethal injection, either as a punishment or a form of euthanasia.
We are first introduced to the concept of release in the beginning of the book when Jonas remembers a plane flying overhead. There is an announcement that the pilot will be released, and Jonas comments on what release means.
For a contributing citizen to be released from the community was a final decision, a terrible punishment, an overwhelming statement of failure. (ch 1, p. 2)
Later, we learn that the only cases where release is not a punishment is release of the elderly and release of a newchild. Release of the elderly is a cause for celebration, and release of a newchild is sad because there is a sense that something else should have been done.
It is not until much later in the book that we find out that release means death.
He killed it! My father killed it! Jonas said to himself, stunned at what he was realizing. He continued to stare at the screen numbly. (ch 19, p. 150)
Until that point, Jonas did not understand what release really meant. None of the community members really did. Jonas was shocked to learn that his father had killed a newborn baby like it was nothing.
Lowry, Lois (1993-04-26). The Giver (Newbery Medal Book). Houghton Mifflin Harcourt. Kindle Edition.