The "release room" is where people are released, which in this community means death by lethal injection. Very few people actually see the release, hence there is a special room for it to be conducted.
The only point in the book where we hear of a specific release room is in Ch. 4 when Larissa is describing Roberto's release. Jonas is curious about where Roberto went when he was released and Larissa shrugs her shoulder and says,
"I don't know. I don't think anybody does, except the committee. He just bowed to all of us and then walked, like they all do, through the special door in the Releasing Room" (Ch. 4).
We also know that all releases are filmed, as the Giver explains this later when Jonas remarks that he wishes he could have seen the release of the newborn twin that his father performed. In that scenario, it does not seem as though there is a specific room for release. Rather, there was an exam room and the release simply took place there.