https://matrix.org is an open standard defining a communication protocol. The goal is to have an open ecosystem where any app can talk to any other app. You can talk to Matrix either natively - or via a bridge. We already have written bridges to IRC, Slack, XMPP and libpurple - if you visit #matrix on freenode you are also talking in the #matrix:matrix.org (https://vector.im/beta/#/room/#matrix:matrix.org) room in Matrix (and vice versa).
You can even connect to Matrix via your IRC client via http://pto.im/
Matrix is decentralised, you can run your own server (clone our server or write your own) and servers will create federated networks on a need-to-know per-room basis (see http://matrix.org/#about).
Matrix is free software, all our code is Apache2 licensed, you can clone it (https://github.com/matrix-org) and use as-it, modify it - or write your own client client and/or server (http://matrix.org/docs/spec/r0.0.1/)!
disclaimer: I work for Matrix.org!