A woman with a blue jacket around her waist is sitting on the ledge of some stone ruins resting.
A woman sits on a ledge
"A woman sits on a ledge" is a shortened version of "A woman with a blue jacket around her waist is sitting on the ledge of some stone ruins resting."
Sitting is a way of resting and stone ruins have ledges.
A woman sitting on the ledge, first has to sit on that ledge.