My understanding is that once upon a time, the governmenet was running out of money (as it does every year), so they said that instead of starting on January 1, the new year would start on Dec. 1 - so that the year that was currently taking place would end sooner, and they wouldn't have spent more than the amount of money they were allotted for that "year" (even if that year ended up being only only 11 months long). And that it happened twice more.
Or, it may have happened all at once - one year it was to end on Dec. 31 and then it was to end on Sept. 30. And somewhere along the line, someone said "Stop! Enough is enough! No more changing the year any more!" And so it has remained as Oct. 1 thorugh Sept 30 ever since.
This could be urban legend though...