The powder is actually tiny scales made from modified hairs. Moths, like butterflies, belong to the order Lepidoptera, which means 'scale wing'. The scales are pigmented but they also contribute to the pattern on the wings by diffracting light through a complex microscopic structure of ribs and holes.
A 2005 study at Princeton University in the US found that the scales showed differences in their structure that depended on their location on the wing and were independent of colour. It's possible they play a role in thermoregulation or modifying the airflow over the wing. If the scales do assist flight, the effect is subtle. Butterflies and moths don't actually need the scales to fly, but their wings are very delicate and if you handle them enough to rub the scales off, you'll probably also damage the wings in the process.
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Protection against the bug zapper?
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~ https://www.sciencefocus.com/nature/whats-the-powder-on-a-moths-wings
What is the point of mud dust on a drywall taper?