A humid night can be defined as one in which the surface temperature drops to the surface dewpoint. A humid night has more relevance as dewpoint increases since a higher dewpoint indicates more actual water vapor in the air. Thus, a true humid night would be one in which the temperature drops to the dewpoint and the dewpoint is above 55 F.
Water vapor in the troposphere acts as a greenhouse gas. As the amount of water vapor in the air increases, the amount of longwave radiation held within the troposphere also increases. When there is not much water vapor in the air, longwave radiation emitted from the earth's surface will more easily escape to space. These nights will result in significant cooling if the initial dewpoint depression is large. Clouds are regions of a high density of saturated air, (which form cloud droplets). Clouds (especially low thick clouds) have a high ability to absorb and re-emit longwave radiation. Thus, on cloudy nights much less longwave radiation is able to escape to space.
When the surface temperature drops to the surface dewpoint the cooling rate is decreased thereafter at night due to the latent heat of condensation release (occurs at surface when dew forms). Once the temperature drops to the dewpoint, the temperature tends to decrease very little beyond that point. This is especially true for air at high dewpoints since much more latent heat release occurs with warm and humid air.
The difference between the high and low tends to be much greater on dry clear 24-hour days than on warm cloudy 24-hour days. This is due to the rate of cooling being greater in dry clear air at night and the rate of warming being greater in dry clear air during sunlight hours.