Discord is the new chat system for the game. If you use voice chat from the game itself instead of something like Steam, you now do that using Discord. I think this also applies to text chat, but I haven't looked into that. AFAIK it also lets you chat to Discord if you want to talk to people there while in the game. And, if you happen to use Discord and want to show off that you're playing the game, it will also update your status in Discord to show you're playing the game.
If you play solo, it's really not needed and you can just disable it in the options. If you use something else for voice chat like Steam, it isn't needed. If you were using Discord for voice chat before, then this improves the experience. And if you were using the in-game voice chat, you'll need to either use this new Discord integration or else find another method to do voice chat.