This add-on adds an extra permission to allow users to delete attachments, assuming that they already have permission to edit whatever content that attachment relates to.
This might be useful if, for example, you have a user who decides to go on a bit of a rampage and edits all of their posts and remove attachments. In XenForo 1.2, the content of the post is safe as all edits are stored, but the attachment would be gone forever (or you would have to find an old site backup to recover it).
This single permission will also apply to other content types -- for example, conversations -- including almost all other content types introduced by other add-ons that allow attachments to be deleted.
Note that when creating a piece of content (e.g., replying to a thread), the user will still be able to delete an attachment they upload before the content is submitted.