* Databases reside on raw disks. There is no file system underneath the databases. If you want a flat file, it has to be in the database. Why? Because databases can be made with good reliability properties and made distributed and redundant.
* Processes can be moved from one machine to another. Much like the Xen hypervisor, which was a high point in that sort of thing.
* Hardware must have built in fault detection. Everything had ECC, parity, or duplication. It's OK to fail, but not make mistakes. IBM mainframes still have this, but few microprocessors do, even though the necessary transistors would not be a high cost today. (It's still hard to get ECC RAM on the desktop, even.)
* Most things are transactions. All persistent state is in the database. Think REST with CGI programs, but more efficient. That's what makes this work. A transaction either runs to successful completion, or fails and has no lasting effect. Database transactions roll back on failures.
The Tandem concept lived on through several changes of ownership and hardware. Unfortunately, it ended up at HP in the Itanium era, where it seems to have died off.
It's a good architecture. The back ends of banks still look much like that, because that's where the money is. But not many programmers think that way.