I am working on bringing Matrix to the WordPress community (see also the WP Tavern post) and part of this is also to explain what Matrix actually is, so I wrote up a few paragraphs that I’d like to share here:
It is open source (Apache License 2.0). Thus it includes the four freedoms (run it for any purpose, modify it, distribute it or a modified version).
When you send messages, these messages are first sent from your client (computer or phone) to the server, from the server to the recipients’ servers (in e-mail, you manually list them, in Matrix, these are all other people in the room), and then the messages are delivered to the individual participant’s clients. The benefit of this is that the client (like a mobile phone app) doesn’t need to be connected when the server receives the message and can catch up when it comes back online.
For this reason, Matrix account addresses look similar to e-mail (or Mastodon) addresses but they have the format @username:server.tld. Starting when a member of a homeserver joins a room, their homeserver will maintain a full, up-to-date copy of the chat room. Any message sent by others in the room will be sent to every participating homeserver. For this reason, joining a room can take a while because the server needs to (partially) populate its local copy from other homeservers. Because of the real-time nature of chat, the messages are exchanged very quickly between the homeservers as soon as that connection has been established.
A Matrix server can also be run in unfederated mode where it will not communicate with other servers on the internet, thus enabling a closed community. This decision can also be made on a room-by-room basis.
Matrix rooms can be either unencrypted and openly discoverable, or end-to-end encrypted and invite-only. Because the server has no knowledge of contents or encryption keys, the latter need to be shared between the individual client software of a user. This is established through a verification step in which you use your other/old client to establish trust with the new one. Until this has happened, any encrypted communication is inaccessible.
The Matrix protocol (and all of its updates, called MSC) is publicly available and can be implemented by any software. There are a couple of server implementations with best known ones by Element themselves, called Synapse (Python based) and Dendrite (Go based). Clients are easier to implement through Matrix provided SDKs that do the heavy lifting of encryption and protocol communication.
Free Choice of Clients
For the above reason, there is a wide selection of clients for mobile and desktop, different operating systems, text based, etc. We have developed a WordPress plugin called Chatrix that allows embedding Matrix inside a WordPress post or page which allows something like we demonstrated in this GIF: