It has to do with the overall set-up within the atmosphere as the rain forms.
Heavy rain usually occurs when the atmosphere is close to saturation from the surface all the way up through the first 10,000 feet, or higher. Lighter rain may form when a thinner layer or two is saturated, but other layers are dry.
But sometimes, a layer of dry air in the middle of the atmosphere can actually enhance heavy rainfall! How is this possible? As warm, moist air rises from the surface, it enters the dry, generally cooler air. Some of the moisture evaporates, as you'd expect. But since evaporation is a cooling process, this middle layer of dry air becomes even cooler. This, in turn, encourages even more of that warm, moist air down at the surface to rise even faster and charge even farther into the sky. It's this fast-rising column of air that can sometimes turn into a thunderstorm and thunderstorms often produce heavy downpours, since so much moisture has been lifted up from the surface as they developed.
Of course, thunderstorms usually only affect an isolated area with heavy rain. When the entire atmospheric column is saturated, a much larger area usually receives a good, soaking rainfall.