Extra-hard is a term used to describe a group of various cheeses that are hard and brittle.
These cheeses get so hard because they are low-fat and low-moisture. In addition to grating well, they are usually aged up to 3 years to develop a sharp flavour.
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.