The auxiliary database refers to the instance that will become host to restored files from the target database in the event of a tablespace point-in-time recovery (TSPITR), a duplication operation (cloning the database), or the creation of a standby database using RMAN backups. When you perform any of these tasks, you will be connecting to the target database and the auxiliary database at the same time from within RMAN. In this way, you can utilize the information about 
the backups in the target database control file to coordinate the restore of those backups to the auxiliary database location. The following shows the connection to both the target database (locally) and the auxiliary database (using an Oracle Net connection):

rman>connect target /
rman>connect auxiliary sys/pwd@aux1

RMAN makes a simultaneous connection to each database and requires access to the SYS.DBMS_BACKUP_RESTORE and SYS.DBMS_RCVMAN packages in both the target database and the auxiliary database. As such, RMAN requires sysdba privileges at the auxiliary, just as it does at the target. Because RMAN must make a sysdba connection to two separate databases, you are required to configure at least one of them with a password file and make an Oracle Net
connection to it.there is no way to connect locally to two different databases.