Sure, the river is Huck and Jim's transportation. It's taking them from captivity (slavery; child abuse) to (hopefully) freedom in the state of Ohio. But the river ends up symbolizing freedom in its own right.
Before hitting the rapids, Huck feels confined—both by both society (which, figuratively, kept Huck imprisoned by its restrictive rules) and by Pap (who, literally, kept Huck locked up). And the river is the only route they can take if they want to be free both in that present moment and in their respective futures. Check out the way Huck describes it:
So in two seconds away we went a-sliding down the river, and it did seem so good to be free again and all by ourselves on the big river, and nobody to bother us. (29)
"Free again," "All by ourselves," "nobody to bother us": to Huck, the river represents a life beyond the rules of society. And that's a life he could get used to.