It’s possible to run the rman utility from a remote server and connect to a target Oracle database via Oracle Net:
$ rman target sys/foo@remote_db
This allows you to run RMAN backups on disparate remote servers from one central location. When you run RMAN remotely, the backup files are always created on the target Oracle 12C database server.
Whenever possible, I run the rman client locally on the target server and connect, like this:
$ rman target /
This approach is simple and adequate for most requirements. You don’t have to worry about network issues or password files, and there are never compatibility issues with the rman client and the target database. If you run RMAN remotely, you need to be sure the remote rman executable is compatible with the target database. For example, you may establish that the remote rman executable you’re running is an Oracle 12c version of the RMAN client and need to determine if it’s possible to connect that client to a remote Oracle 9i target database. If you run the rman client locally on the target server, there is never a compatibility issue because the rman client is always the same version as the target Oracle 12C database.