It looks to me like stone cladding. Round here it is mostly like an ornamental tile nailed or stuck to a brick wall, but in some areas, such as parts of Yorkshire, houses are built with an outer leaf of real or reconstituted (concrete) stone blocks.
Your damaged one seems to have sand and small stones in it, suggesting it is a concrete material, but I am not familiar with the material.
Indian sandstone is quite popular now.
Why do you want to clean it?