Its an open standard for communications (like xmpp, but the new hotness) with a focus on federating IRC chat. (lot of cool work on state resolution by them wrt that). So you can communicate with people on different matrix servers as long as they federate with each other. Additionally, they have built in support for bridges that let you connect to other people via matrix giving you a seamless experience on that service via matrix. Lemme know if you need more clarifications.