The full quote, which is in chapter 16, is "came the dawn! ... Came the dawn—God, what a dawn!" He's basically referring to the fact that a new day is just approaching, and they are beginning in the worse way possible. In addition, he is signifying a change in their circumstances. Mildred is losing her business, and Veda may never sing again.
Earlier on in the chapter, Mildred arrives home at three in the morning, looking for her daughter, Veda. She knocks on her husband Monty's door, but from the doorway, he says he hasn't seen her. Mildred is about to leave him to go to bed when she realizes that he is trying to block her view of something. She flicks on the room's light and sees her daughter lying naked in Monty's bed. Monty tries to excuse his behavior by stating that Mildred had only married him to use him as "bait to attract the errant Veda." However, Mildred just slumps down in her chair and stares straight ahead.
It is only when Monty and Veda start to leave that Mildred jumps on her daughter and begins to strangle her. By the time Monty drags Mildred away, she has damaged Veda's vocal cords so much that Veda, an opera singer, can no longer sing. It is at that point that Mildred slumps down with the realization of what she's just done to her daughter, and Monty says, "came the dawn," ending the chapter.