Discord's feature for setting a short personal message below your username is called Custom Status.
A Custom Status lets someone write a brief message about what they are doing, feeling, or planning. Users can also attach an emoji and choose when the status should clear, such as after a set period or one day. It is separate from Discord's standard presence choices: Online, Idle, Do Not Disturb, and Invisible.
A common mix-up is Activity Status. Activity Status describes something Discord detects or displays as a user activity, such as a game or connected service. “About Me” is instead a profile biography field, while “Bio” is an informal description rather than the official feature name.
Custom Status has changed in presentation over time, but the name remains the same in Discord's own Help Center. It can override how an activity status appears in some member lists, although the underlying activity may still be visible when someone opens the full profile.