Symbolism, Imagery, Allegory
Because Gabriel is a baby and can't talk or emote in any discernible way (adorable gurgles don't count) he's really more of a symbol than a full-fledged character. You can't be a character if all you can do is be crazy-cute.
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:
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.
He was aware of giving the memory; but suddenly he realized that it was becoming dimmer, that it was sliding through his hand into the being of the newchild. Gabriel became quiet. Startled, Jonas pulled back what was left of the memory with a burst of will. He removed his hand from the little back and stood quietly beside the crib. (14.76-77)
All the more reason to try and protect him, right? 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.