People have tried to explain this a a meteor shower, sun dog, fata morgana, or a small comet breaking up in the atmosphere.
The meteor and asteroid fit in some ways as descriptions of objects on fire falling to earth then vanishing into steam fit a meteor strike very well.
Given the times the descriptions of crosses and balls of lights could just be imagination related to religion.
Fata morgana doesn't works if some reports that the objects "filled the skies" are true, but many say it was at sunrise and the objects appeared near the sun and it would fit the description of the large black object reported at the end of the event. Also that is an issue for the meteor/asteroid ideas because the descriptions are so chaotic. Even if hundred or thousands of meteors were coming into the atmosphere would would think there would be more organized direction described, not streaking about as if in combat. But if they were coming in from the direction of the sun it could explain the varying descriptions as people try to look into the sunrise to figure out what they see.
No really detailed description has ever been found that I know of, The paper reported it with a religious slant. If you do a search for Switzerland 1566 you will find a similar report but of black circles. Could be the same phenomenon just reported with a different perspective, but again at sunrise.
2 existing woodcuts depict the event but they differ starkly. The color woodcut is much like the event describes but the black and white woodcut is much like the description of the Swiss event. The Swiss account sounds like what you might expect to see if the sun was behind a meteor shower coming over the horizon.
Another interesting theory is some sort of time slip, that these people were witnessing the events of WWII somehow playing out in the skies above them.