Answer:
Pleural mesothelioma attacks the lining of the lungs, known as the mesothelium. When asbestos fibers are inhaled or ingested, they make their way to the lungs, lodging in the mesothelium.
Asbestos fibers are particularly difficult for the body to breakdown, as it would with other foreign object inside of the body. The body fails to chemically breakdown the asbestos, leaving it in the lungs to cause further damage.
Pleural mesothelioma is not curable and there is a whole lot of study-in regards to histologic findings. The attached article goes into more detail about pleural meso specifics including, cause, care, etc.