To babble is to talk on and on without a particular goal. It might drive you crazy when your little sister babbles endlessly about her favorite video game.
Babble sounds like Babel, the Biblical tower where everyone was talking in their own language. Everyone was babbling without paying attention to their neighbors, like the kid who won’t stop talking about his trip to the water park three years ago. A stream or a brook can babble, too, but that’s more of a soothing sound of water against rocks. Babies gurgle, because they don’t have enough words to babble yet.