Are “permissions”, (sorry, old Unix term), used with Linux?
If so, would you please discuss their significance to the security of a system?
Yes, permissions are used in Linux. They are granular enough that you can assign individual users to have rights on individual files.
If so, would you please discuss their significance to the security of a system?
Every process runs "as a user" of some sort--whether that is an actual user or a service account. Each account is assigned groups and permissions. As a normal user on a linux system, I would not have permission to delete or modify some system files, for instance. As the Apache user, I can run everything needed to operate a web server, but not really anything else.
For a piece of malware to perform any real damage to a system, it would have to run with elevated privileges--typically root. If I download a piece of malware, it would usually "belong" to me--that is it would have the same privileges I do. That is why you should never surf the web, or log in as root. If the malware were to run, it would only be able to damage my user account, rather than the system as a whole.