I always understood the term to mean those Irish folks with dark or black hair, as well, and a slightly darker complexion than the red-headed Irish (Light tan, rather than pink-white)... but neither of African nor of Mediterranean descent, which are some of the theories explored in the link above.

According to my mother (I think she's the one who introduced me to the term... she's 13 years dead, so I can't double-check -- and I'm not sure where the information came from, in any case), they are descendants of the ancient Celts who inhabited the islands before the fairer-complexioned Norse invaded and set up trading posts in the southeast.

The article above was the first place I'd seen the "Survivors of the Spanish Armada" theory. As someone who's dabbled a bit into Irish mytholothy, however, I recognize the Spanish from "The Book of Invasions," which was a mix of history, legend and mythology compiled by monks in the 12th century. According to this "Book", the Tuatha de Danaan, a god-like people who helped shape the landscape of Ireland, came to Ireland by way of Spain (the monks were redacting Irish myth to fit it into Biblical and political history) -- certainly a lot earlier than the Spanish Armada! The Tuatha later built and retreated into the "fairy mounds" when they lost the battle with humans over control of the land (they survive today as the "fairies" or "Fair Folk" in more recent folklore).

Now, it's just my hunch, but if this "survivor of the Spanish Armada" does stem from an imperfect memory of a small detail in a 12th century text, it might lend support to the idea that the "Black (haired) Irish" are indeed descendents of early natives of the islands.