I used ES a long time ago and rivers have since been deprecated: https://www.elastic.co/blog/deprecating-rivers

A river was just a mapping from a database to ES. For example, you could search CouchDB with ES with the proper river set up.

In Elasticsearch a "river" is the description for the pushing of data from your primary store (A database more than likely) into the elasticsearch index.

ES actually started with Rivers being part of Elastic but since deprecated it. You will still find people talking about "rivers" though as a description for however they are updating the index.