The photographers' 'Blue Hour' is the period of twilight each morning and evening where there is neither full daylight nor complete darkness.
The time is considered special because of the quality of the light. Some photographers call it sweet light.
It typically occurs 30-90 minutes before sunrise and after sunset, in northern latitudes. It is much shorter in the tropics and it depends on cloud cover.
As a result of the perceived specialness of this time, there are various restaurants, theatres and hotels called L'Heure Bleue located worldwide.
There is also a women's perfume by Guerlain (1912) of the same name.
The drinkers' 'Blue Hour', was a term in British culture used to describe a period of afternoon inactivity.
This occurred when pubs had closed after lunch-time (~3:30 pm), but had not yet opened for the evening session (~6:30 pm).
It has now been largely abolished in England, Scotland and Wales in favour of all-day opening.
The Blue Hour is also a film directed and written by Eric Nazarian.
It stars Alyssa Milano and had its world premiere at the San Sebastián International Film Festival in 2007. Reference: Wikipedia
For a blue-hour photography calculator see: http://www.bluehoursite.com