TWRP, or Team Win Recovery Project, is a secondary "miniature" operating system on its own partition. So is Clockworkmod. What this means is that should Android fail for any reason ("brick", boot-looping, etc), you can key into your recovery software and restore a backup. Nandroid backups are exact backups of your system's partition tables, where it stores the operating system and such, and can restore a device to the exact state it was when you backed it up.
I'm a visual learner, too. I apologize that I cannot help more, as I don't have a Galaxy S4 so I cannot create video tutorials for you.
Lord of the Snarkô
Tempest [OmniROM] 4.4 (Manta) (m7att)