From Nookipedia, the Animal Crossing wiki
A river is one of the six types of water in Animal Crossing, the others being the sea, the lake, the pond, and the waterfall. They stretch from one side of the town and empty into the sea at the other. A river begins as a waterfall at an edge of town and passes through the town. In all towns, a river flows through a lake. Some towns have a river that splits in two, creating an Islet. There are usually two or three bridges crossing a river. Fish can be caught in the river.
|Type of geography
In Animal Crossing: New Leaf, rivers can be shaped differently. They always begin at the east or west of town, instead of the north.
The river mouth is the area where the river meets the sea. Some fish can be caught only in this particular spot. In some towns, there may be two or more of these, increasing the chances of catching these fish.