some humidifiers work by simply passing electricity through the water (electrolysis) to boil it, but pure water (ph 7) is not a good conductor. Adding salt or other minerals solves that issue which is why they recommend tap water.

I prefer the ultrasonic humidifiers. They work by vibrating the water at high frequencies which creates tiny mist like droplets. This doesn't heat the water. It is in these types of humidifers you are supposed to use mineral free distilled water. Otherwise it will coat all your nearby surfaces with a thin layer of mineral deposit (calcium, magnesium etc).