Well, from what I've done so far with trading stocks and options (have NOT gotten into futures) here is my best guess for what happened.
The fake crop reports fed to the brothers called for an absolutely abysmal outlook for oranges - the crop was going to be devastated.
So, they took their money and their margins (I have a brokerage account with a margin - an amount the brokerage will lend me to make trades with. If the stocks, options, or futures you bought with margin do badly enough, the brokerage sends you a margin call - you need to add money to keep the losing bets going. If you can't or won't add more money, they force-sell what they need to in order to balance out the books. I have margin, but have avoided using it) and bought up every futures contract the could - using cash, margin (and since they had chairs on the brokerage's board, they may have had an insane amount - or almost limitless amount - of margin) and whatever other resource they had. Since they "knew" those futures were going to be worth a ton once the report was made public.
Some saw what the brothers were doing and started buying too - driving the prices up further.
Eddie and Dan waited until the frenzy had driven up prices to crazy levels and then sold all the futures they had bought up *the day before* - also with whatever amount of leverage they had. Very short term options on the futures would let them control a huge amount of "shares" for surprisingly little money, so what they had to work with went a long way. They just waited until prices reached, say, 10x what they started the day with, then sold all they had at, say, 9x. Unloading it all in a heartbeat for a huge profit.
The real report comes out, and it is the opposite of the fake one - there will be a huge bumper crop of oranges - and futures are now really worth next to nothing.
Futures prices plunge, as everyone who followed the brothers tries to unload the overpriced futures at once. They cannot sell off enough, for enough, fast enough, and get the dreaded margin call - with the results shown in the movie.
I'm sure there was originally a lot of explanation of what was actually going on and why, but all of it was cut to make the movie more enjoyable - if more mysterious.