Matrix is:
an open standard for decentralised communication, providing simple HTTP APIs and open source reference implementations for securely distributing and persisting JSON over an open federation of servers.
It's pretty fantastic, if you think on the massive problem of fragmentation all across the web. They've created an easy to use API, and you can do a kludgy test using curl from the terminal (*nix, mac, win). See: http://matrix.org/docs/howtos/client-server.html
It's pretty straightforward to do a quick test. I have an account at https://matrix.org / https://vector.im, so I used that to get a token.