Symbolism, Imagery, Allegory
There's a lot you could say about the river and symbolism, and none of it is necessarily right or wrong. You could go with the "you can't step in the same river twice" argument, which is to say that the river symbolizes change, an important idea in Jonas's static community. Or, you could say that river symbolizes the boundary between Jonas and the rest of the world. On the other hand, rivers flow, right? So it could be about the river flowing out, away from Jonas's community, in the direction he will eventually take himself. Then again, there's a lot of death associated with the river – first with the child Caleb and later as the site of Jonas's planned fake death. Jonas first thinks of release as escape from the community, and later learns that release is really death, so the river is, in a way, both about leaving the community and about dying. Funny, because that's what the ending of The Giver is about, too.