Harmonic singing is used in sound therapy to create a change, either in the physical body or in the mental state of the listener.
Harmonics are present in any form of singing but, in harmonic singing, the singer creates stronger resonances around selected harmonics by shaping the throat very differently than does a classic singer. This particular singing technique highlights frequencies that are already present in the voice, but would remain unnoticed without the extra emphasis.
This emphasis serves as a metaphor for the process of healing. You may be getting better, but not yet be aware of it. Sometimes, it only takes listening to a sound to flip a switch in the mind. This is the intrinsic nature of sound healing.