The wait button lets you hold off in hope of better weather. If it is raining or snowing and you have a lot of archers that you want to use, then it might be a good idea to wait in the hope that the weather changes.

I seem to remember reading pre-launch that night battles would not be possible, but you could fight at dusk. Not sure where I read this--maybe on Gamespot. If you wait until you can't wait any longer, you will notice the light dimming as the sun gets lower.