# sit in the dust, virgin daughter of Babylon; sit on the ground ... daughter of the Chaldeans.

Sitting in the dust was a sign of humiliation.

# virgin daughter of Babylon ... daughter of the Chaldeans

Both of these phrases refer to the city, Babylon, which is spoken of as if it were a daughter. That the city is a "daughter" indicates how people think fondly of her.

# without a throne

"without the power to rule"