First of all, we should note that it is a little cold-blooded to talk about positive effects of this horrible human tragedy. We should not lose sight of the fact that millions of people died due to the Black Death.
That said, we can say that something good came of it for the survivors. Because the Black Death killed so many people, there was much more demand for the workers and peasants who survived. They were able to get better wages and working conditions and such after the Black Death. This helped to improve their standard of living and it also helped to give them more power over their lives.
So, while the Black Death was really a terrible thing, it did open European society a bit to people who used to be on the bottom. It made it easier for them to get a good wage for their labors and it made it easier for them to gain more control over their lives rather than being tied to a given piece of land.
I am not dictating any of these results of the Black Plague as "good" or "bad", but many of them were within the cultural, literary, artistic, and religious aspect.
Firstly, there was an upsurge of renewed religious enthusiasm. The “mechanism of infection” of diseases was not common knowledge in the 1300’s. As a result, people turned to religious meaning and many people believed that only the anger of an all-powerful being could have caused such widespread pain and suffering as a result of human sin.
The plague also had a massive impact on the art and literature that came out of the generation that went through it. It was often more melancholy and depicted sorrowful scenes of death and destruction, even in poetry and other forms of writing.
In the long run, lots of Europeans lost their faith in any kind of religion during and after the Black Death. This was because they spent days praying for their god to remove them of the punishment they believed was the plague, and asked for forgiveness of sins they believed had caused it.
In stark contrast to the times of Roman conquest, when Christianity spread to the poor with promise of reward for a good life, the people affected by plague heard no response and felt no passion, and saw no reason to continue. Hundreds of thousands of people went through this at the same time there was a religious upsurge. The effects rippled through Europe and religion was no longer the biggest focus of people’s lives. Instead of living for an afterlife, they began to live for “the now”, which was also reflected in the art of later periods, going into the 15th century.