What is the significance of the river in "The Deep River"?

The river in the story symbolizes the community that lives around the river and the change that comes with the migration. Bessie Head compares the community to the deep and steady river but also talks about the change that comes when the head of the tribe dies—because rivers move and have currents as well.
Head writes that "the people lived together like a deep river. In this deep river which was unruffled by conflict or a movement forward, the people lived without faces" because they aren't worried by things like personal pride or accomplishment. Instead, they work together to make a good life for everyone. This is embodied in the chief of the tribe and is one reason why things are in such upheaval once the chief dies. He makes all the decisions, and then one day he is gone, and the community is left to function without him.
When this happens, it's revealed that the chief's oldest son and heir was in love with the chief's last and youngest wife; he also fathered her child. People urge him to choose a different wife, but he'll only have her, even though it worries his brothers because it changes the line of succession. The community is in upheaval, and these events ripple through it and make the river of the community less steady than it once was.
The chief's son is almost convinced to set his wife and their child aside. Sebembele decides to claim his wife and child, however, and is expelled as the leader of the tribe. The people—the community—decide to stay loyal to him and travel with him because he embodies the characteristics that make them want to give themselves over to him. Like a river, they travel as one and set up a new community together.

In Bessie Head's story, the river represents the Talaote people; it is a symbol of the collective will and purpose of a close-knit community.

Long ago. . . the people lived together like a deep river. In this deep river which was unruffled by conflict or a movement forward, the people lived without faces, except for their chief, whose face was the face of all the people.

The river is deep, perhaps also representing the depth of the people's commitment to their communal way of life. The old traditions of common ownership and cooperative economics are long-standing, and that is why Sebembele's stubborn loyalty to Rankwana and Makobi is seen as a rebellion of the worst sort. Others even view Sebembele's love as unnatural and a masculine aberration (divergence or departure from what is considered normal).
We are told that Sebembele's actions constitute the "first ripples of trouble" stirring "over the even surface of the river" of the villagers' lives. In the end, Sebembele chooses to leave the village with Rankwana, Makobi, and other villagers who support their chief. So, the deep river is significant in that it represents the Talaote community and the collective will of the people. However, a river can also be split into what are called distributaries, smaller streams or rivers. The process of splitting is called river bifurcation.
In the story, Sebembele represents a "distributary" that has split from the main, deep river. His actions highlight the realities of individualism and the fate of a community divided by strife.

They accepted this regimental leveling out of their individual souls but on the day of dispute or when strife and conflict and greed blew stormy winds over their deep river, the people awoke and showed their individual faces.