What does Genesis 16:10 mean?

The angel of the Lord found Hagar at a spring along the road, possibly on her way back to her homeland in Egypt. She was fleeing from the harsh mistreatment by her mistress Sarai, and she was pregnant with Abram's first child (Genesis 16:6). Sarai's abuse came in response to Hagar's contempt for Sarai, which itself was caused by Hagar immediately conceiving a child for Abram, when Sarai had been barren for decades. Abram allows Sarai to assert her ownership over Hagar, and as a result, Hagar runs away.

After telling Hagar to return and submit to Sarai, the angel of the Lord now makes a familiar promise to this slave girl. It's familiar because it's the same promise the Lord made to Abram himself multiple times over the last few chapters. Specifically, that He—this angel of the Lord—will multiply Hagar's offspring so that they become uncountable. Of course, only the Lord Himself could likely make such a promise. This is a primary reason most scholars presume this "angel of Yahweh" to be a theophany, the Lord Himself in a physical form.

All the same, this child is not the promised heir for Abram and he will not inherit the blessings which God has guaranteed for Abram's descendants. In the following verses, this promise is followed by a prophecy explaining that the future is not entirely good news for Hagar and her unborn son, Ishmael.