Jonas’s community has found a way to contain memories. The memories are a collective consciousness. They are the community’s history, and they are stored in the Receiver of Memory. Each Receiver eventually becomes a Giver, passing the memories on to the next Receiver when he is twelve years old.
Being a Receiver of Memory is “hard and painful work” and there is no relief-of-pain medication (p. 76). Jonas receives memories of pain, famine, war and everything else that makes up the spectrum of human experience. All of these memories have been collected over time “back and back” through their collective history.
The Giver tells Jonas that the community made the choice to go to sameness a very long time before.
“We relinquished color when we relinquished sunshine and did away with differences." He thought for a moment. "We gained control of many things. But we had to let go of others." (p. 95)
As a result of giving everything up, people no longer know where they came from. If they knew their history, they might feel uncomfortable. The community does whatever it can to avoid discomfort. So they sacrifice pain to the Receiver of Memory so the Receiver can hold their memory. It is in this sense that memory is forever.
Lowry, Lois (1993-04-26). The Giver (Newbery Medal Book). Houghton Mifflin Harcourt. Kindle Edition.
In "The Giver", the memories that people have are always around, they are permanent. Because they can be viewed as dangerous for people in they community they are all kept by the Giver to help and advise the community. When a Giver dies they do not die with him; they will come back to the people living in community. They are therefore transferred to the trainee, in this case Jonas. When Rosemary chose to be released the memories she had not transferred to another Giver were released back to the community and there were many problems. Memories are forever, they are permanent - if they aren't going to be with the Giver then they will be with the people.