Discord seems to be a nice mix between live messaging programs like Skype supporting both one one one or group chatting using multiple channels.
It also have VoIP capabilities including group VoIP so you can chat with others using your voice instead of just typing.
Another nice feature of Discord is that it allows easy connection with your streaming/capturing applications so you can easily share you screen with others even when you are playing games. This has made it especially popular amongst game developers as you can play the game and show them in what scenarios some bugs might happen.
I have also seen Discord even being used by some companies for online tutorials about using of their software.