What the mechanism actually is
Red and near-infrared light in roughly the 600–900 nm range penetrates skin and is absorbed by structures inside your cells, including cytochrome c oxidase in the mitochondria. That absorption is associated with changes in cellular energy production and signalling — which is why the field is properly called photobiomodulation rather than 'light healing'.
This is not a fringe idea. Photobiomodulation appears in peer-reviewed dermatology, sports medicine, and rehabilitation literature, and light-based devices have been cleared by regulators for specific uses such as treating wrinkles and relieving minor muscle and joint pain.