This is one messed-up clock. It doesn't actually tell time, it puts on semi-pornographic and riot-inducing shows, and it becomes the centerpiece of a very bizarre new religion: tiktokism, which seems to promote having a good time and using machinery.
So what is really going on with this wacky clock? Well, let's get a sense of what this thing looks like first.
It is nothing more than a tottering, freestanding theatre.... On the flat roof is a clockwork dragon, an invention of green painted leather, silvery claws, ruby jeweled eyes. Its skin is made of hundreds of overlapping discs of copper, bronze, and iron. (1.2.5)
The clock doesn't tell time; instead it tells people secrets from their past and present and predicts their future. Elphaba gets a private viewing of her very own life story with the clock and sees the legend of her namesake, the truth of her paternity, and a future shrouded in darkness. Oddly enough, the dwarf gives her back her mirror as a parting gift, perhaps suggesting that Elphaba should use it to divine her own future.
But while Elphaba's clock-told life story seems fairly accurate, the clock often exaggerates and even outright lies. It seems to demonstrate that people can't really be trusted to respond well to either truth or lies. And the clock is an interesting hybrid of many of the major themes (power, communication, fate, evil) and religions (the myth of the dragon that dreamed the world, tiktokism) in the book.
As a hybrid of themes and symbolic imagery, it's no wonder the book's other hybrid, Elphaba, is born inside the clock and likened to a young dragon during her childhood. If a dragon is lying beneath the earth, dreaming everything up (1.6.65), then perhaps Elphaba herself has more power to determine the shape of her world than even she realizes.