Fossiliferous (yes, that is a word) limestone forms from organism rich sediments or coral reefs in usually shallow marine environments. Shells of small marine organisms are most often formed of calcium carbonate. In time, the weight of the accumulated shells and sediments cause a gradual sinking of the material. With additional sediments constantly accumulating, the weight from above causes compaction of those sediments, squeezing out air and fluids from the space between the shells and shell fragments. These particles are cemented together by the mineral calcite which precipitates out of the remaining fluids. The compaction and cementation are part of the process of lithification, or rock formation.