Cornering the market is a (generally illegal) form of market manipulation where someone buys or controls enough of something--a stock, commodity, etc.--so as to effectively control the market price for that item. It can be very profitable, since the person who has cornered a market can force buyers (at least those buyers who have no alternative) to pay essentially any price.
For example, you might corner the market in frozen concentrated orange juice by going out and buying up all the OJ you can find, then entering into contracts with the OJ plants to buy their production. At some point, someone wanting to buy frozen concentrated orange juice would be forced to come to you, and pay whatever price you ask.
In practice, there may actually be more OJ futures available to buy in the market than actual OJ production, since a significant fraction of the market is not actual buyers or sellers of the physical commodity but speculators who trade futures contracts expecting to close their positions without ever touching any actual juice (except perhaps at breakfast). So when those futures contracts start to mature, the speculators discover that they are obligated to deliver actual frozen concentrated orange juice (which is unavailable) or buy back their contracts at some absurd price. You have, in effect, created an artificial shortage of OJ to your own benefit.
Cornering a market is very expensive, since you have to have enough capital to lock up most of the supply. It can also be very risky, since if you try and fail to corner a market, you can wind up paying too much for a huge amount of something you don't actually need. Nevertheless, every so often someone tries to corner a market; and occasionally someone succeeds.
The most profitable, and most difficult, market to corner would be the market for money itself. Money is in some respects a commodity like any other: it can be bought and sold, you can create derivatives, and you can write contracts which obligate the delivery of a certain amount of money under certain conditions. If you could corner the market for money, you would drive up the value of money (otherwise known as "deflation") by creating an artificial shortage (aka "liquidity crisis"). The people you traded with would be unable to deliver the money they were obligated to under their contracts, so you would be able to demand whatever other hard assets they might have instead.
Cornering the market in money would be hard, but maybe not impossible. The best way would be to buy up a whole lot of some financial contract which is normally relatively inexpensive, but under the right (very rare) circumstances obligates the seller to give you a hundred or a thousand times the capital you invested. Ideally, the seller would view the contract as safe (so the price would be low), but could be triggered by some crisis.
A Credit Default Swap (CDS) fits the bill pretty well: pre-2008, you could buy a contract for a few tens of thousands of dollars per year which would obligate the seller to give you $10 million upon the failure of some big investment bank or blue-chip corporation.
So you buy CDSs on a bunch of big low-risk corporations at 2006 prices (which is to say, dirt cheap). Since the CDS isn't directly tied to an actual bond issued by the company, you can actually buy more CDSs than the company has outstanding debt. Then, recognizing that there's a cascading effect, you also buy CDSs on all the companies who sold you the first set of CDSs--since if Lehman Brothers has to pay out on all those swaps, they'll have a good chance of defaulting as well. Since the CDS market is almost completely opaque, nobody will know how many contracts you've bought up or what the aggregate value is.
At 2006 prices, you could have invested a few billion to buy CDSs which would pay (in aggregate) a trillion dollars or more if the companies started failing. Lots of investors have a few billion to throw around. Almost nobody--other than the U.S. Treasury which prints its own money--has a trillion.
The corner happens when one of the companies you bought CDSs on starts getting into a little trouble. Every company has rough spots, so this is bound to happen sooner or later. That will make the market value of the CDSs you own go up, and lets you demand more collateral from the companies you bought the CDSs from.
That, in turn, requires those companies to come up with cash quickly, and hurts their financial stability--which drives up the value of the CDSs on those companies, and lets you demand more collateral from a different set of counterparties.
If it all plays out right, in fairly short order every company which sold you CDSs is selling every asset they can get their hands on in order to meet their contractual obligations to you. Cash becomes the most valuable commodity because nobody can find enough of it. It's financial armageddon, but you win big.
The only flaw--and it's a big one--is that the government can create new cash any time they want. Normally they don't like to do this, because it can lead to inflation. But if the government discovers what's going on early enough, they can print more money, give it to the foolish companies who wrote those CDSs (like AIG) to make good on their promises, and break the cycle of collapse by making money less scarce. This excess cash can (at least in theory) be taken out of the system at a later date once things have stabilized, in order to prevent hyperinflation.
So....do you bet on the Federal Reserve being on top of things and pumping the cash to the right place at the right time? Or do you bet that nobody will figure out what's going on until it's too late?