What does Isaiah 10:21 mean?

This chapter has described how the Lord will use Assyria to bring judgment on His people in Israel and Judah for their faithlessness (Isaiah 10:1–4). The Lord will turn and bring judgment on the Assyrians for the arrogance of their kings (Isaiah 10:15–19). Now, Isaiah describes how Israelites who survive this judgment will once again trust the Lord. They will no longer look for help from other nations (Isaiah 10:20). God's people will once again lean on the Holy One of Israel, their God.

The prophet says that the remnant of Jacob will return to the mighty God. In writing this, Isaiah was essentially using the name of his own son. This is the son he took with him to visit it King Ahaz in Isaiah 7:3: Shear-Jashub, which means "a remnant will return." This return will be the fulfillment of the prophecy contained in the name of his own child.

Isaiah might be pointing to the temporary return to faithfulness in Jerusalem when the angel of the Lord wiped out the Assyrians surrounding the city in 701 BC (2 Kings 19:35). Or he may be pointing further into the future when a remnant of Israelites will return to Jerusalem from captivity in Babylon. This is recorded in the books of Ezra and Nehemiah.