What does Genesis 21:9 mean?

The joyful arrival of Isaac as the keeping of God's promises to Abraham and Sarah is clouded by the existence of Abraham's older son Ishmael, perhaps 16 years old now. This is not the first time Sarah has reacted with anger and hurt feelings towards Hagar and Ishmael. That prior incident complicates our understanding of Sarah's actions in this passage. Sarah is partly responsible for Ishmael's place in their family. She was the one who had convinced Abraham to try to have a child with her servant girl in hopes of having her own child by proxy (Genesis 16:1–2). Almost immediately after it worked, however, Sarah had become outraged with Hagar's new status in Abraham's life and her contemptuous attitude (Genesis 16:4–6).

Now that Isaac has been born, it seems, Sarah simply cannot bear to have either mother or son around any longer, as will become clear in the following verses. She would have reason to be concerned, on one level, that Ishmael would somehow take Isaac's place as Abraham's heir.

On the day of the great feast thrown by Abraham to celebrate Isaac being fully weaned, Sarah sees something that upsets her. She sees Ishmael—"the son of Hagar the Egyptian"—laughing or mocking. The text is not clear what exactly is meant about Ishmael's laughing. It's possible that he was simply laughing or even playing with Isaac. Given the response described here, it's more likely that he was making fun of something, perhaps even ridiculing little Isaac in some way. Whatever he was doing, it was enough to make Sarah angry.