n the literature it seems that I would point my application to a MySQL router (mysqlrouter) instead of directly to the MySQL database

That is correct. Basically, as far as your application is concerned, mysqlrouter is the mysql server, so you connect to that and send requests to it as if if were a standalone database. mysqlrouter will then decide which backend server(s) each request should be sent to (based on availability, loading, type of query, etc.) without your application having to know or care about these details.