You mean a "day" in-game? I believe that goes by the actual RL date the message was sent. So that would change at Midnight server time. (i.e. 6 hours after the sunset turn (also known as the half turn)).
@Velax: The forum timestamps messages according to the time zone settings you have set in your forum preferences. By default it is set to German time, the same as the game server. But if you change that to your local time zone, then it won't match server time anymore.