The main reason why Discord is so popular is because of their amazing support for chatrooms, moderation, bot support and other customisability. Slack is also good in this regard but they don't support voice channels and require the owner to pay for his or her server pretty quickly unlike Discord where paying for a server is not really needed unless you want to have access to some more customisability.

And when comparing it to Telegram it is a lot different like @semobo said Telegram is more similar to Whatsapp as a general chat app in which you can also have group chats.