Symbolism, Imagery, Allegory
Because Gabriel is a baby and can't talk or emote in any discernible way, he's really more of a symbol than a full-fledged character. So what does Gabriel symbolize? Well, to Jonas, Gabriel is a pal. Jonas identifies with him. There's that whole light eyes thing (and we have more to say on that in a bit) and the fact that they can share memories together. But why does Jonas choose Gabriel to share the memories with? Because he's a baby, and because he's in danger of soon being released, Gabriel in many ways exists outside the rigid control of the community. Jonas can't transmit memories to Lily because she's too ingrained in the "people shouldn't touch other people" mantra of the community. Gabriel, however, is untainted; he's pure and free.
All the more reason to try and protect him. Because Gabriel hasn't yet come under the thumb of the community's control, he's also a symbol for a brighter future. When Jonas escapes with Gabriel (maybe, unless they die), we get the sense that there is hope for us all.
There's also something to be said about Gabriel's name, but for that you're going to have to check out "Tools of Characterization." See you there.