Sentence:  The stone of which this town and church was built, is somewhat of the nature of "rotten limestone,"—is quite light in color,—<WSD>quarries</WSD> out regularly and easily,—is soft, when first <WSD>quarried</WSD>, but becomes hard on exposure to the air. 
Meaning of the word marked with <WSD> tags:  To obtain (or mine) stone by extraction from a quarry.