The archive contains an additional function: It is not possible to delete something in the lists of newsletters, subscribers, campaigns, mailing lists and templates. Deleting only is possible in the archive. Here, too: Mark the desired to delete in the appropriate tab at the select box and click on Delete at right top. Here also you have to answer a confirmation prompt. And also an additional question appears at campaigns to delete the assigned newsletters or not, too.
For deletion the permissions View archive and Delete are necessary.
Before deleting You should reflect, if You possibly have obligation for verification or retention and the subscriber may not be deleted finally.