Linux server getting error as no space left on device while copying

i am using few AIX unix server for my company.we used to take the server backup and for that reason we shut down the services and instances before the backup.we kept the screenshots of the services before the backup.once the backup is over we used to bring up the services but last day while bringing up the services we got and error as “no space left on device”.can anyone suggest why we are getting such errors.
