This message may appear on attempting to restore a backup in SQL Server Management Studio (SSMS). An "Access is denied" result on a restore operation generally indicates insufficient permissions to perform the operation. Please consult your local IT staff for assistance granting the necessary permission. Note that permission often needs to be granted to the service account that SQL is running under (the end-user's permission level is not relevant).
https://support.microsoft.com/en-us/kb/224071 (see "Scenario 3")