Well, to save myself a couple sentences explaining what it brings to the table compared to the other big programs used for gaming/party chat:
A friend came across this program a while ago and it is a lot more user-friendly than the others. TeamSpeak has a lot of hoops you have to jump through to set up a server (not to mention it looks like a Windows 98 program) and Skype has been getting more bloated and annoying.
Discord's servers are set up in a way similar to Skype's chatting, but with a separate text/voice channel setup, kind of like a modern TeamSpeak. The dev team specifically built it to give gamers a haven from Skype and TeamSpeak specifically.
Oh, and did I mention you don't have to download it to use it? It has a browser client, too! You can just set a username and get into it without even registering (though registering is required if you want to reserve that username for future use)