How is moaning caverns formed made?

Moaning Cavern is a solution, or karst, cave formed as all such caves are, by dissolution of calcium carbonate by slightly acidic ground-water. In this case the rock is marble, metamorphosed limestone, but still the same chemical.

Try just putting its name in Wikipedia as I did to answer this - it also tells you the origin of its name!

It is a show-cave now, offering as many show-caves now do, "adventure caving" as well as the straightforward walking tours.