This tag for Jerusalem
appears some four dozen times in the Bible. The phrase has its origin in the fact that David (with his men) captured the stronghold of the Jebusites (2 Samuel 5:7–8). In Nehemiah’s work the phrase appears twice, both times in connection with these stairs (see also Nehemiah 12:37). That would suggest that there is no particular (theological) significance to this phrase being used in the present context; it is simply part of the nomenclature that belongs to these stairs.
15 And Shallum the son of Col-hozeh, ruler of the district of Mizpah, repaired the Fountain Gate. He rebuilt it and covered it and set its doors, its bolts, and its bars. And he built the wall of the Pool of Shelah of the king’s garden, as far as the stairs that go down from the city of David.