To burble is to move with a rippling flow, the way water bubbles down the side of a small garden waterfall.
A stream burbles as it travels along its bed, bubbling over rocks and branches. The verb burble captures both the movement of the water and the sound it makes as it moves. You could also say that a brook or stream or river babbles or ripples or even trickles. The word burble was first used in the 1300's, and it probably comes from an imitation of the sound a rippling, bubbling brook makes.