Rivers move lily pads in the direction of the water flow. Lily pads can hold Cropsies and other surprises such as Squirrels and Goats. For every move the player makes, the river will move the lily pad (and whatever is on top of it) one space in the direction of its flow.
Tip: The river cannot be controlled, but its movement is predictable, so use that knowledge to your advantage! Sometimes you won't need to make a match if the river's movement will create the match for you automatically after your next move.