Night time usually symbolizes calm and peace. In The Night Circus, I think thats what it symbolized at night everything was serenity. It also was used to depict some character's personalities. Like the circus performers, able to do all that magic and illusions.
"It was that glorious hour, with the daylight still glowing everywhere, but the moon already gleaming and the first bats dipping in the green, shimmering air. On the edge of the woods stood dissolving in the last light, bright chestnut trunks against black shadows. A yellow cottage softly radiated the daylight it had absorbed, glowing gently like a topaz. The small paths pink and violet, led through meadows, vineyards and woods..." - Hermann Hesse