The Desert Ruins are the grounds where three Desert Sirens roam.
When Kratos came across the Desert of Lost Souls, killing these three Sirens was required before being allowed pasage. Doing so would open up a doorway into a set of ruins within the desert.
The first part of the ruins consists of hall with a moving conveyor belt and a spiked crusher at the end. Beyond that, is a chamber with two murals. One is of the Gods ordering Pathos Verdes III to construct Pandora's Temple, and the other is of the temple being chained to the back of the Titan Cronos. Outside that chamber is a horn, and a giant "wall" of blowing sand. Blowing on the horn reveals a path through the sands to a second horn, which Kratos blows to call Cronos.