Gabriel, the small child that Jonas's father brings home to nurture, represents family and hope to Jonas and to the readers. For starters, he represents family. Jonas quickly notices that he and Gabriel have those light colored eyes in common. He even wonders if they had the same birth mother (which would make Gabriel literally his family!). Gabriel unknowingly teaches Jonas to love, which was basically unknown to Jonas. Gabriel cries at night, and Jonas is the only one who can calm him. This allows Jonas to step into a nurturing family role, which is something that would happen naturally in our society, but was not allowed in theirs.
Gabriel also represents hope for Jonas and the readers. He is young, and innocent, and provides Jonas with the strength and courage he needs to escape from their society of Sameness. Jonas loves Gabriel, and this gives him hope that life can be better like he's witnessed in his sessions with The Giver. Because Gabriel has become family, their only hope is to leave in order to save Gabriel's, and ultimately Jonas's life. Their journey and ultimate freedom give them the hope they need to continue on until they reach their destination.