I'm new to TWRP, but here's my question: why would you prefer TB or any other software over the Backup feature from TWRP?
Mostly because TB will allow you to flash another rom/a clean flash of a rom and then restore your apps and/or their respective data. This is helpful if you screw up the rom and it becomes unbootable, infected, slow, etc...and you want to start fresh or swap to a new rom without losing your app data (especially for the majority of us who don't want to give all of our personal data to Google through Google app backup).
TWRP Backup/Nandroid is great for backing up your ROM and reflashing it back to the exact state that it was at, filesystem, data, and all, in the case of screwing something up and effectively needing to undo what you did.