5 May - Denmark's Liberation Day
4 May 1945 was the day when the Danes got the message on the radio about the liberation of Denmark from Germany during Second World War, after the German occupation since 9 April 1940. This meant that the Danes no longer had to use heavy black curtains to keep the light from getting out of their houses. People flocked into the streets, waving the Danish flag “Dannebro” and burned their black curtains. Many lighted candles on their windows.
Therefore, if you see candles on the windows in the evening of 4 May, it is because Danes celebrate and commemorate this day.
The message about the Danish liberation went out on 4 May, but the official liberation day is 5 May. It is celebrated with flags in flagpoles and on top of the busses.
If you are interested to know more about this day, here is a fascinating article about the occupation of Denmark.