Nitrogen beers are beers that use a larger percentage of nitrogen in the carbonation process. The ratio is usually around 70 percent nitrogen to 30 percent carbon dioxide and those are the gases that actually carbonate the beer when they come out the draft. Nitrogen beer is most closely associated with the dry Irish stout but these days, many beers are being nitrogenated. You'll find IPAs are that are nitrogenated, ESBs. Really, all kinds.
What the nitrogenated beer is really known for is it's very soft and persistent head and it winds up being very creamy because of the very small nitrogen bubbles that are in the nitrogenated beer. This can have the effect of dulling or muting some of the flavors in beer, so there are some people are really opposed to using the nitrogenated beers for many different styles.
But, at the same time, you can account for that in the brewing process so there's really no rights or wrongs around should you nitrogenate the beer as a brewer. It really does give the consumer, the drinker, a totally different experience in drinking.
Nitrogen beers, they're being found more and more often. They're more than just the dry irish stout, and if you see one on draft at your local bar, I suggest that you try one. You'll see what that creamy, smooth mouth feel is like.