Limestone can be simply thought of as calcium carbonate (CaCO3). Acid rain contains sulfurous acid, sulfuric acid and nitric acid. When these acids reach the Earth's surface, through acid rain, they react with the limestone and dissolve it. The following chemical reactions take place:
`CaCO_3 + H_2SO_4 -> CaSO_4 + H_2CO_3`
`CaCO_3 + 2HNO_3 -> Ca(NO_3)_2 + H_2CO_3`
etc. In all such cases, the limestone reacts with the hydrogen ion and forms the carbonic acid, which breaks down to yield carbon dioxide and water.
`H_2CO_3 -> H_2O + CO_2`
This causes the breakdown and dissolution of limestone. An example is the dissolution of limestone that makes up the famous monument, Taj Mahal, in India.
The acid rain is due to human activities, especially the use of fossil fuels, manure handling, etc.
Hope this helps.