Certain trades are obvious winners- index funds available for less than the sum of their component parts for example. Everyone on the street knows they are obvious winners, so usually the trade isn't available for long. Firms have computers set up to constantly scan the markets for these opportunities. Whoever sees the trade first and gets to the exchange first ends up making all the money.

But that sounds to me like it should be called low-latency trading, not high frequency?

Right so far :-) But the HFTs are not in the game for the long haul; they will immediately sell the stock to another investor, at a price between what the HFT paid for it and what the stock is worth to the other investors. That's why it's high-frequency trading. The buy and sell are almost synchronous.

Caveat, I'm not a finance guy, but my understanding is that on a short time scale you can predict the price direction of stocks under certain conditions.

For example, if I notice that there are several large orders buying a stock, I can assume that a large institution is trying to purchase a position. If you reach this conclusion quickly enough, you can buy up enough stock, temporarily hiking the price, and selling the stock back to the large institution as they are trying to fulfill their purchase order. Do this enough times, and for large enough orders, and you can make money.

Here's a very good presentation that describes what HFT is and how it works (and some of the myths):

http://www.tradeworx.com/TWX-SEC-2010.pdf

how does tradeworx compare to jane street capital?

It's not a Martingale system because at very short time-frames traders can predict price movements much better than 50%. I think the fancy term is statistical arbitrage.

I believe at a certain scale the markets actually pay a fraction of a cent per trade to encourage liquidity.