The Giver transmits memories to Jonas through his Capacity to See Beyond.
We do not know exactly how the memories work. We know that they are stored in people with the Capacity to See Beyond, and that they can also be transmitted to people who have that ability. A Receiver of Memory also needs other traits, including intelligence, integrity and courage. These traits help the Receiver deal with the memories and use them to the community’s advantage.
When The Giver transmits a memory to Jonas, all he does is touch him and think about a memory. Then the memory is transmitted to Jonas, and he loses it himself. The memory passes from one person to another.
The Giver tells Jonas to lie face down and remove his tunic. Then he puts his hands on his back and transmits the memory.
"I am going to transmit the memory of snow," the old man said, and placed his hands on Jonas's bare back. (Ch. 10)
The Giver tells Jonas that just transmitting one memory lightens his load. He continues to give Jonas a variety of memories, both positive and negative. Jonas develops emotions, and learns to see and identify colors. His life completely changes.
Jonas discovers that he has the ability to transmit memories as well as receive them when he accidentally sends a memory to Gabriel.
Still patting rhythmically, Jonas began to remember the wonderful sail that The Giver had given him not long before: a bright, breezy day on a clear turquoise lake, and above him the white sail of the boat billowing as he moved along in the brisk wind. (Ch. 14)
Jonas is not even aware that he is giving Gabe the memory, but the baby calms. Like Jonas, Gabriel’s pale eyes indicate that he has the Capacity to See Beyond.
The Giver has all of the communities memories, given to him by his Giver. His job is to advise the community based on the past, because the community has chosen to ignore the past except for the memories. The Receiver of Memory protects the community from any strong emotions. Only he or she knows pain, love, or fear.