There are times when you want, or have to, give the administrator full access to all the exchange mailboxes. This is f.ex the case when you want to restore an email in Veeam directly into the mailbox for the user. The default Exchange permission will just give the users access to their mailboxes.
You can give individual access to users by delegating the access in the Exchange ECP (2013), but to apply this to all mailboxes you can use the following powershell command
Get-MailboxDatabase -identity «[mailbox database name]» | Add-ADPermission -user [username] -AccessRights GenericAll