The red dot on your Apple Watch indicates unread notifications. When your iPhone is locked but your Watch is unlocked, alerts are sent to the wearable instead. The dot appears until you view and dismiss the notifications.
To clear them, press and hold the watch face to open Notification Center. Swipe left on any alert and tap 'X' to dismiss, or scroll to the top and tap 'Clear All' to remove everything at once.
If the indicator causes anxiety, disable it entirely via the Watch app on iPhone: go to Notifications and toggle off 'Notifications Indicator'. You can also mute specific apps by swiping left on their alerts, tapping the ellipsis, and choosing 'Mute for an hour' or 'Turn Off'.
Most apps mirror iPhone settings, but some offer custom options like 'Send to Notification Center' to silence alerts while still collecting them.
Source: Engadget · Summarized by HeadlinesBriefing