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The blue hour is the period of twilight each morning and evening when the sun is a significant distance below the horizon and the residual, indirect sunlight takes on a predominantly blue hue.
This effect is caused by the relative diffusability of short blue wavelengths of light versus the longer red wavelengths.
During the blue "hour" (typically the period is about 40 minutes in length), red light passes straight into space while blue light is scattered in the atmosphere and therefore reaches the earth's surface.
The morning blue hour begins when the geometric center of the sun is at -6° of elevation and ends at -4°. In the afternoon, it begins when the sun is at -4° and ends at -6°.
The effect was discovered and explained by Lord Rayleigh an english physicist.
During the day the clear sky is blue according to Rayleigh, ozone has little effect on the color of the daylight sky. But near sunset and throughout twilight ozone affects the sky color profoundly.
For example, in the absence of ozone the zenith sky would be a grayish green-blue at sunset becoming yellowish in twilight, but with ozone the zenith sky is blue at sunset and throughout twilight (as is observed), the blue at sunset being due about ⅓ to Rayleigh and ⅔ to ozone, and during twilight wholly to ozone.
Because of the quality of the light, this period is treasured by photographers.