rqlite gives you the functionality of a rock solid, fault-tolerant, replicated relational database, but with very easy installation, deployment, and operation. With it you've got a lightweight and reliable distributed relational data store. Think etcd or Consul, but with relational data modelling also available.
You could use rqlite as part of a larger system, as a central store for some critical relational data, without having to run a heavier solution like MySQL.
rqlite replicates SQLite for fault-tolerance. It does not replicate it for performance. In fact performance is reduced somewhat due to the network round-trips.