“The south side.” That is, the south side of the tribe of Benjamin.
“went out to the spring.” The border is now traveling east (a little southeast).
“spring of the Waters of Nephtoah.” This spring is just on the outskirts of the modern city of Jerusalem. This description, that the border of Benjamin goes from the Waters of Nephtoah to Kiriath-jearim is exactly the opposite of the description of the north border of Judah, which runs from Nephtoah to Kiriath-jearim (Josh. 15:9)