Unsubscribe means unsubscribe from letter (as I see, for example, you are subscribed to receive messages to an email when someone replies).
Record(s) found - database records.
Subscriptions - the link for administrator, clicking on it, admin can see the list of subscribed users to the topic.
"Within last" - simply the general phrase. Used with combination of "days" so because it is splitted by input text field (see in search and statistics).
Moderator is the person with high privileges level, similar to admin, who can edit, delete and move any topics and posts, but can not enter the admin panel.