The 'Dropbox External Share' detection rule aims to identify instances where shared Dropbox items are being shared outside the allowed domains. It checks whether users are adding non-team members to shared files or folders, which could potentially lead to data exposure or breaches. The rule is triggered if an external email (i.e., an email not included in the allowed share domains) is associated with the sharing event and the user is attempting to grant access. The expected result is to flag these actions for investigation by cybersecurity professionals to ensure adherence to data sharing policies and mitigate risks associated with unauthorized access.