The first one is the moon phase, the second one is the weather (clear sky or one of the elements).
Currently, it is unknown whether moon phase has any effect on game play. Maybe some mobs/NMs appear at certain times. I'm sure they will implement something more in the future.
Elemental weather likely has something to do with the effectiveness of elemental spells. Again, if this hasn't been implemented yet, it will likely be in the future.
Edited, Jan 10th 2011 1:43am by Threx