Basically, having Jonas around has convinced the Giver that change is possible. Jonas has made him think change is possible and has given him an idea as to how to bring it about.
About 3 or 4 pages into Chapter 20, the Giver tells Jonas that he has come to believe that change is possible. He has thought for years that things should change, but it is only since he's worked with Jonas that he has thought it is possible and indeed necessary.
He has gotten this idea by listening to Jonas's ideas about feelings and things like that. They have made him realize the community is really missing something. Then, when Jonas talks about what might happen if he (Jonas) died, the Giver started to think about the possibilities of how losing Jonas would change the community.
After watching his father kill a newborn baby through lethal injection and dump the body down a chute as part of his job as a Nurturer, Jonas is distraught. The Giver announces to Jonas that the two must make a plan, acknowledging that the world has not always been a place in which people are devoid of feelings; there used to be pride, sorrow, love, and pain.
Jonas' ability to share the memories of these feelings with the Giver is what has given him hope that it is possible for things to change. The two talk for a long time and finally reach the conclusion that Jonas must try to escape the community to go Elsewhere, an act which would mean that the residents of the community must "bear the burden themselves," accepting all of the emotional memories that Jonas had been storing for them. The Giver will stay behind to help transition the community into accepting these memories and to prevent them from destroying themselves once they feel the great, communal weight of having those feelings returned to them.