The Hebrew name Asshur can refer according to context to the ancestor named in Genesis 10:22, the land or people of Assyria, or the Assyrian realm associated with the ancient city of Assur. This requires some care when interpreting individual passages.
Numbers 24:22 refers prophetically to Asshur in Balaam's oracles, while Ezekiel 27:23 names Asshur in a description of the extensive trading relationships of Tyre.
The city itself is important for biblical history because it gave its name to the Assyrian civilization that later became one of the dominant powers confronting Israel and Judah.