tl;dr: Airports like to sell drinks (and it may increase security)

As described by @jpatokal it is indeed possible to make explosives out of some liquids, and thus airlines used security as a reason to ban all liquids.

Though the amount of terrorist attacks prevented by this is probably in the range of 0-1 (which could of course make it worth the effort), there is a side effect that is easily noticeable:

Since it is harder for people to arrange their own drinks, the number of drinks purchased at an airport increases. I have been unable to find a citation for this but can attest to this from personal experience.

So, preventing people from taking bottles may increase security, but it will definitely increase revenue. And this is at least part of the reason why the rule got enough support to be implemented.

The policy is actually fairly reasonable, and the base reason is that they can't run an analytical chemistry laboratory at the checkpoints (nor find staff that can both understand the results and work for a government salary).

The hydrogen peroxide mentioned in another answer is one possibility. Looks just like water. The stuff you buy at the drug store makes a great antiseptic or toothpaste, stronger mixes make good rocket fuel. Gasoline looks a lot like apple juice - light up 500ml of Regular Unleaded and ask yourself if you want that happening in the window seat. 100ml bottles of apple juice are rather rare and will attract attention. Other chemicals not mentioned here can start roaring blazes on contact with air - you just have to open the cap.

Sales were certainly not a consideration - every airport I've been to charged market rate for drinks after security, one openly advertises (since the 1990s) that prices after security are exactly the same. And I've had no problems at all bringing a freshly rinsed thermos through. It gets a quick glance to see if its empty.

If you ask them, it's to prevent terrorist attacks in the form of bombings. Apparently several people posting agree. I would answer that it is to appear to prevent terrorist attacks. I say that because tsa is slightly more effective than mall cops.
Could there be bombs created through that nefarious methods that get caught by the liquid limitations? Maybe. Probably not. TSA got caught missing something like 95% of things getting past them by homeland security. So hope it's that 5%. It isn't like multiple people couldn't pool together small bottles of liquid.
The purpose is to appear busy and to make people feel safe by being very intrusive. The reason we haven't seen more attacks is because of increased intelligence operations, and because we reinforced the cockpit door. Without the ability crash the plane into something, we're back to the pre-911 days, where they can attack the plane, but it's not nearly as good a target.

Nitrated alcohol looks so like water. One good shake can blow all away.