Extra-hard is a term used in the cheese world to describe a group of various cheeses that are hard and brittle.
Cheeses in this grouping become very hard because they are low-fat and low-moisture. They are usually aged up to three years as well.
In addition to grating well, they typically have a sharp flavour from the aging.
Some versions of extra-hard cheeses may be sold when they are younger as semi-firm cheeses.
Extra-hard cheeses were developed as low-moisture and low-fat cheeses precisely so that they would store and ship well. If you wrap a piece of extra-hard cheese well, and refrigerate it of course, you should be able to store it for up to a few months.