In TS/Mumble/Vent terminology, there was no federation (unlike IRC), so a server was generally literally a single server hosted somewhere. All the channels, all the users, etc, went to a single machine.
Discord's selling point isn't really being a "better IRC", it's the voice chat. It's a better TS/Mumble/Ventrillo. Low-latency, decent audio quality, push-to-talk or an actually functioning level detection, with an easy to use interface. It's "Chat for Gamers" for a reason, not "IRC with history".
True, but you had to pay for a server for TS/Vent/Mumble as well, so the $5/month Discord charges for the higher voice quality is comparable (or cheaper).
Discord is voice chat, with text as a nice extra, and with image/file sharing and screen sharing and emoji/stickers/profiles (these are attractive to some people). IRC is text only. TS/Mumble/Vent were all voice chat, with really awful text chat interfaces (TS was sort of OK, Vent may as well not have had text chat).
I don't think Discord is good as an information archive, and I'm not terribly fond of seeing FOSS projects using it as a primary means of communication, but it's great for gaming compared to what we had before.
Discord's selling point isn't really being a "better IRC", it's the voice chat. It's a better TS/Mumble/Ventrillo. Low-latency, decent audio quality, push-to-talk or an actually functioning level detection, with an easy to use interface. It's "Chat for Gamers" for a reason, not "IRC with history".