What is muscle balance therapy exactly?

Quackery. Therapy to improve your balance is great. But "muscle balance therapy" is a proprietary system of therapy aimed to treat people with low back pain. However it has never been extensive studied or validated as an appropriate treatment for low back pain.
Resetting you... Balance board therapy has a variety of uses; and aiding in overall core stability and muscle retraining is among them. Discuss this with your doctor; and a physical therapist is you need to. Cheers!