My wife was reading about it a few days ago. I’d never heard of it. The Blue Moon is much more familiar, the second full moon in a month, something that happens every two years or so. It’s something you can see on the 31st, the 30th, and very rarely, on the evening of the 29th of the month.
The Black Moon is rather the opposite: the second new moon in a calendar month.
As seen from the Southern hemisphere, the black moon partially blocked the sun the other day. That’s about the only time we get to see a black moon, otherwise it’s too close to the sun to get noticed.
If we counted full moons in liturgical seasons, it would be easier. Lent always has two, and Easter always just one. Advent sometimes has none, and never two.
Catholic Sensibility 
IIRC, there’s a new moon during the weeks in which Ash Wednesday, Ascension Thursday and Sacred Heart Friday fall, and a full moon in the week headed by Pentecost Sunday.