The Wikipedia entry just gets more and more nightmarish:
At the time, Mrs. Crouch, a farmer’s wife, was making soap on her porch when she reported seeing the meat pieces fall from the sky. She said she was 40 steps from her house when the meat started to slap the ground. The meat looked gristly, according to Mrs. Crouch. Mrs. Crouch and her husband believed the event signified a sign from God. A similar event was later reported in Europe. The phenomenon was reported by Scientific American, The New York Times, and several other publications at the time.
Most of the pieces were approximately 2 by 2 inches (5 cm × 5 cm); at least one was 4 by 4 inches (10 cm × 10 cm). The meat appeared to be beef, but according to the first report in Scientific American, two gentlemen who tasted it judged it to be lamb or deer. B. F. Ellington, a local hunter, identified it as bear meat. Writing in the Sanitarian, Leopold Brandeis identified the substance as Nostoc, a type of cyanobacteria. Brandeis gave the meat sample to the Newark Scientific Association for further analysis, leading to a letter from Dr. Allan McLane Hamilton appearing in the Medical Record and stating the meat had been identified as lung tissue from either a horse or a human infant, "the structure of the organ in these two cases being almost identical." The composition of this sample was backed up by further analysis, with two samples of the meat being identified as lung tissue, three as muscle, and two as cartilage.
Brandeis's Nostoc theory relied on the fact that Nostoc expands into a clear jelly-like mass when rain falls on it, often giving the sense that it was falling with the rain. Charles Fort noted in his first book, The Book of the Damned, that there had been no rain. Locals favored the explanation that the meat was vomited up by buzzards, "who, as is their custom, seeing one of their companions disgorge himself, immediately followed suit."