“People of my wrath” is a phrase from Isaiah’s prophecy against Israel, quoted by Nephi in his record (2 Nephi 20:6). It names the nation the Lord had marked for judgment: a “hypocritical nation” whom He would punish through foreign conquest.
In the prophecy the Lord sends the king of Assyria against this people as the instrument of that judgment: “I will send him against a hypocritical nation, and against the people of my wrath will I give him a charge to take the spoil, and to take the prey, and to tread them down like the mire of the streets” (2 Nephi 20:6). The surrounding verses call Assyria “the rod of mine anger” and note that the Assyrian king himself does not intend to serve as God’s instrument, but means only to destroy nations (2 Nephi 20:5,7).