Apparently it works by hosting HTTP or Websocket microservices and communicating between them via JSON.
The .clio files transpile to JavaScript, and the project optimistically targets full JS interoperability (e.g. compatible with any of your favorite npm modules).
Thanks to the portability of JSON, clio can import functions from any compatible microservice, including those written in other languages. For an example of this, see: https://github.com/clio-lang/python-microservice-example
Besides reading the tutorial, I found this source helpful to understanding how Clio knits the microservices together: https://github.com/clio-lang/clio/blob/develop/host/host.js