Parmigiano-Reggiano is considered the King of Cheeses in Italy. Once you've tried real Parmigiano-Reggiano you will never want to go back to the abomination we Americans call "Parmesan."
Benedictine monks started making this cheese in the middle ages for its long maturation. Parmigiano-Reggiano is named after the province of Parma in Italy. It is made from partially-skimmed cows milk in the Italian provinces of Parma, Reggio Emilia, Modena, and parts of Bologna and Mantua. The process takes over 12 months, and each wheel of cheese is inspected before it can be sold by a battore. The battore strikes each wheel of cheese several times with his hammer, listening for structural imperfections. Any wheel of cheese that doesn't pass is stripped of its external markings and is not allowed to be sold as Parmigiano-Reggiano.
Parmigiano_Reggiano is often used as a grating cheese over pasta and other dishes, but it is excellent as a table cheese.
The Consorzio del Formaggio Parmigiano-Reggiano is the consortium that regulates and controls the quality of Parmigiano-Reggiano. They have an excellent website. We recommend watching their video on how Parmigiano-Reggiano is made. (To get there, click on "English," then under the "The Cheese" menu item, choose "How It is Made.")
Where to buy
You can find Parmigiano-Reggiano in most quality grocery stores. Don't buy it pre-grated. It's much better when you grate it immediately before eating it. Also, make sure you get cheese with the "Parmigiano-Reggiano" dotted stamp in the rind, so you know that your are getting the real stuff.
If you want to buy some online, pastacheese.com and amazon.com have several Parmigiano-Reggiano cheeses. Amazon sells from many different vendors, so make sure you are buying the real stuff. (Hint, make sure it says Parmigiano Reggiano, not Parmesan, and make sure to read the product description.)