A watcher follows an issue without owning it. They see it, they are told when it changes, and they are not the person being asked to do the work.
This topic includes:
What a watcher can do
A watcher can see the issue and is notified when it changes. Watching does not grant the right to edit fields or reassign the issue — those follow from the member's role, not from watching.
Add watchers
Pick them under Watchers when creating the issue, or on the issue's own page afterwards. Watching widens who hears about an issue; it does not override anybody's own notification preferences, so somebody who has muted the Issues tool stays muted.
Assignees become watchers
Assigning an issue to somebody adds them as a watcher automatically — being asked to fix something implies following it.
Note: if the assignment later moves to somebody else, the original assignee stays a watcher. They were involved, and they usually still want to know how it ends. Remove them by hand if that is not what you want.