We currently host static renderings of the notebooks, for reading and sharing, where you can pull them down to your local installation of Jupyter to extend them.
On our roadmap is for Kyso to work like the Google drive integration, where you can use a jupyter kernel (https://github.com/jupyter/jupyter-drive) hosted anyway but server the notebooks from Kyso.
And we are also planning fully runnable notebooks too, we do aim to be the easiest way to run your own jupyter server.