It's almost a complete mystery. The facts are that the vellum dates to the early 1400s via c14 radiocarbon dating. The manuscript gets its name from Wilfryd Voynich, a bookseller in New York who purchased it in 1912 from the Collegio Romano, where it had likely been kept as part of Athanasius Kircher's collections since his death. Voynich discovered it with a letter to Kircher from one Jan Marek Marci in 1666. Marci inherited it from his friend, an alchemist named Georg Baresch, and claimed that some 50 years prior it had been purchased by the Holy Roman Emperor Rudolf II for 600 ducats (quite a lot of gold). Baresch had been interested in deciphering it and in 1639 had sent copies of a few lines to Kircher - a renowned polymath who'd published a dictionary of Coptic and erroneously claimed to have decoded Egyptian hieroglyphs. Some modern researchers had thought that Voynich fabricated the manuscript and the letter, but carbon dating and the discovery of the 1639 correspondence puts that pretty much to rest.

As to who wrote it, what it says, and whether it even says anything at all; no one knows. There's been a lot of attempts at understanding it as a cipher (including by members of the NSA in the 60's, interestingly), and arguments about whether or not it's a natural language or a construct or pure nonsense or even very carefully constructed nonsense. Several methods of statistical analysis have been conducted with contradictory results

If you go to this website and search for Voynich you'll get a pretty decent selection of papers on it.

One of the more interesting ideas I've seen is that it might be related to a Nahuatl herbary. Interesting and strange theories about it are a dime-a-dozen, however; see this list.

Basically, no one in the last 400 years has been able to unambiguously prove anything at all about the main body of the text and its illustrations. I think it could possibly be the result of a really exceptional case of forgery or even mental illness.