The Managing/Watching option lets Managers and Watchers of any workflow view and administer workflows. The details of the workflow instance displayed is same as the other dialogs with an important distinction.
If you are designated as a workflow manager, you can also perform administrative operations like transitioning the workflow to next steps, delegating the current workflow task to another user or canceling a workflow. Workflow managers are users or members of a group that has been assigned the managers role during the creation of a workflow.
Members of the Watcher role can only oversee the progress of a workflow instance but cannot change anything but they can send a personal reminder for an overdue task by right-clicking on a task and selecting 'Send Email Reminder'.