The short answer: open Discord's User Settings (the cog, bottom left) › Voice & Video and lower Output Volume. For one loud person, right-click them and lower their slider.
Discord's own volume
- Everything in Discord: User Settings › Voice & Video › Output Volume. This changes Discord only.
- One person: right-click their name, in the member list or in a voice channel, and drag their volume slider.
- The soundboard: User Settings › Voice & Video › Soundboard. Set it to 0% to silence other people's sounds.
Attenuation, and why it may not be there
On Windows, Discord's Attenuation turns other apps down while someone talks. Discord's help doesn't say whether it works on a Mac, and Mac users report the setting is missing. Look in Voice & Video; if it isn't there, Discord can't change other apps' volume on your Mac.
With Sordina
Sordina puts a slider for every app that's playing in your Mac's menu bar, so you can set Discord against everything else in one place. That part is free.
- Click the Sordina icon in the menu bar.
- Drag Discord's slider, or click its mute button.
- Everything else stays where it was. Discord keeps its level until you change it.
It works the other way round too: if Discord is fine but your game or music is too loud, turn that app down instead.
Long gaming sessions and Calls
Sordina Pro's Calls turns other apps down while any app uses the microphone, and Discord keeps the microphone open the whole time you're in a voice channel. If you game in one all evening, right-click Discord in Sordina's panel and choose Ignore During Calls. Your game then stays at the level you set.
Common questions
One person is much louder than everyone else
Right-click them and lower their own slider. It only changes how loud they are for you.
I can't hear one person at all
Their personal slider may have been turned down by accident. Right-click them and check it.
Everything in Discord sounds wrong
In Voice & Video, the Debugging tab has Reset Voice and Video Settings, which puts Discord's audio settings back to their defaults.