The Irish potato famine of the 1840's led to mass migration from western Ireland to America.These migrants were unlike the earlier migrants in that they were catholic and usually Gaelic speaking. As such they were seen as foreigners and a threat and were discriminated against.
They found themselves in a similar social position as Black Americans.

It's important to point out that the term black would have had little to do with colouring. It's a common american misapprehension that some european populations are exclusively dark or fair or that they are divided somehow along those lines. Hair and eye colour as well as skin tone vary,for example Swedes are stereotyped as blonde and blue eyes, but only a minority of them are both blonde and blue eye. Blonde or red hair is in a minority in every european country.
The term "Black Irish" has no meaning in Ireland.