“the River.” A common biblical idiomatic name for the Euphrates River. The people rejected the water in Judah, so metaphorically the water of Assyria will flood upon them, as the Assyrians attack. The Assyrians will overflow their channels and banks and flow out of Assyria and into Israel and Judah. The Euphrates River was much larger than any river in Israel, and it was known for its sudden and violent floods.
“the king of Assyria.” Isaiah had already foretold the invasion of the Assyrians privately to King Ahaz (Isa. 7:17-20), now, in Isaiah 8:1-7, Isaiah declares it in a very public way.
“in all his glory.” Edward Young writes, “Accompanying the king of Assyria would be all his glory. In their historical inscriptions, the Assyrian kings often spoke of the power of the glory of their might as overwhelming the enemy” (Edward J. Young, The Book of Isaiah, Vol. 1, chapters I-XVIII, NICOT).