When Moses was born, the entire house filled with light. According to Sotah 12a, his mother Yocheved saw immediately that he was special—the Torah's phrase "she saw that he was good" (Exodus 2:2) is the same language used at Creation: "God saw the light, and it was good" (Genesis 1:4).
But the backstory begins with Amram, Moses's father, who had separated from his wife when Pharaoh decreed that all newborn boys be drowned. If there was no point in having children, why bring them into the world to be killed? All the Israelite men followed his example and divorced their wives.
His daughter Miriam rebuked him. "Your decree is harsher than Pharaoh's," she said. "Pharaoh decreed only against the boys. You have decreed against the boys and the girls, because no children at all will be born." Amram remarried Yocheved. The other men remarried their wives.
Miriam had also prophesied: "My mother will give birth to a son who will save Israel." When Moses was born and the room flooded with light, Amram kissed Miriam on the head: "Your prophecy is fulfilled." But when they placed Moses in a basket in the Nile, Amram struck Miriam on the head: "Where is your prophecy now?"
That is why the Torah says Miriam "stood afar off, to know what would be done to him" (Exodus 2:4)—she was watching to see if her prophecy would come true.
The passage also explains why Miriam appears in Chronicles under the name Azubah—"the abandoned one." She was sickly and unattractive. No one wanted to marry her. Caleb married her for the sake of heaven, ignoring her appearance. The Torah credits him "as if he gave birth to her"—meaning his devotion transformed her. Her face, the Sages said, eventually became beautiful as a rose.