The black death was a vicious, brutal disease and health pandemic that swept over Europe in the 1300s. One in every 3 Europeans died in the infestation.
The black death was spread by rats. This made the infection very easy to migrate within regions, as rats were littered all over the place in those times when Europe was a very dirty, non-sanitary place. Furthermore, there was virtually no way to stop the spread of disease, as long-distance communication was nearly impossible, given the technology (or lack thereof) of the time.
As for the Catholic Church, I don't know of anything about the black death that would have influenced it. The Church had already been in existence for 1300 years preceding the pandemic. And, of course, the Church did not "perish" because of it.
The only thing about the black death that I can think of relating to the Catholic Church is that the virus was often spread as a result of over-crowded Churches. Lockdowns were oftentimes issued for infested cities - people were required to stay in their homes to avoid spreading disease. However, Sunday (and even weekday) Church was not included in the lockdown, thus Churches frequently became far too crowded, speeding the spread of the infestation.