In The Giver, what did Jonas give to Gabriel and why did he give it to him?
In chapter 14 of Lowry's The Giver, Jonas gets up in the middle of the night to check on a whimpering baby Gabe, who has been staying in his room. Jonas touches Gabe to soothe him and daydreams about a calming memory of a sailboat on beautiful blue water. Unwittingly, Jonas passes that memory onto Gabe who quiets down in response. At first, Jonas isn't quite sure if the memory transferred and if it was the reason Gabe quieted down. However, Jonas has another opportunity to verify whether he can send soothing memories to Gabe during the early morning hours when the baby wakes again. The entire memory of the sailboat didn't transfer the first time Jonas touched Gabe, though. In an effort to discover if he has the ability to transfer memories to Gabe, which in turn will soothe the baby, the following is described:
Again Jonas went to him. This time he quite deliberately placed his hand firmly on Gabriel's back, and released the rest of the calming day on the lake. Again Gabriel slept (147).
As a result of this experiment, Jonas learns that he has the ability to deliver a memory to Gabe, then Gabe is able to receive the memory, and the result is a calming effect on the baby. This is important to know because Jonas uses this knowledge of his skill to help him transport Gabe away from the community, especially useful when they face unbearable obstacles such as hunger, fatigue, and cold and stormy weather.
I think what you are talking about is how Jonas gives memories to Gabe. He does this for different reasons at different times.
At first, the reason Jonas gives Gabe memories is to help him sleep. Gabe is a restless baby and Jonas is afraid he will not be able to get placed with a family if he won't sleep well. If that happens, he'll be released. So Jonas gives him soothing memories.
Then later, when they are running away, Jonas gives Gabe memories of snow to make him colder so that the airplanes' infrared detectors won't be able to "see" him.
When Gabe comes to their house, Jonas realizes he is there to learn how to sleep through the night. If he doesn't, Jonas is told, he'll be released. Jonas sees something different about Gabe and wonders if Gabe can receive memories...and if Jonas can give them. So he asks his parents if Gabe can sleep in his room, and they agree.
He experiments with giving Gabe pleasant memories to help him sleep, and it works. He later gives him memories to keep him quiet as they are escaping and again to keep him warm as they are in the snowstorm.
Jonas gives "memories" to Gabe. He learns how to transmit memories. He first transmits memories to solve Gabe's sleeping problems at nights. The other time he gives something to Gabe is also "memories". He transmits memories to Gabe when they escape from the community, he transmits again some memories to prevent Gabe from the bad weather and hunger.