RMAN backup command is nicely explained HERE
Theory behind RMAN Backup & Recovery is explained on the page Backup & Recovery
To list (have a quick look of) all the data that need backup, expired backups, stored scripts, incarnations… we should use LIST command in RMAN, as explained HERE
If we want a more detailed analysis, we use report command, as explained HERE. Report command gives us information on what needs to be backed up, which backups are obsolete, information about db schema and any problems that it detects.