The region around Rome produces large travertine deposits that have been exploited for thousands of years. The stone is generally solid but has pore spaces and fossils that give the stone character (see an example of travertine building stone in the Limestone Picture Gallery). The name travertine comes from the ancient deposits on the Tibur River, hence lapis tiburtino. See more photos and learn more detail in the Travertine Picture Gallery.
"Travertine" is sometimes used to mean cavestone, the calcium carbonate rock that makes up stalactites and other cave formations.
For more photos see the Sedimentary Rocks Gallery.