Rigate means “ridged” in Italian, and is often used in conjunction with pasta shape names to differentiate them from their “lisce” or “smooth” cousins. Whether it ends in an ‘e’ or an ‘i’ depends on the preceding word. It just has to match, so it’s penne rigate, but pennoni rigati.
Almost any shape can be rigate – penne rigate and rigatoni rigati are some of the most common, but even long cuts like spaghetti and fettucine or special shapes like large shells (conchiglie rigate) are made in ridged form. The ridge creates a minute topography of peaks and valleys on the surface of the pasta, which helps trap sauce and make it “cling” to the pasta.