"Front running" is a name for placing securities trading orders ahead of already known orders. It's a way for some people to take advantage of other people. Someone sees a large order in queue, and is in a position to place an order ahead of it.

How can that happen?

Well, it's happened in a small fashion throughout history. There have always been "specialist traders", and they have tended to maintain orderly market flow, and market liquidity.

Front running has become a different animal with the advent of computerized trading. There is a reason why it's called "front running". It's possible to jump the queue and trade in advance of others' large trade orders.

There are various ways to take advantage of that. For example, upon seeing a large buy order, jump in and buy ahead, wait for the large order to jump the price, then dump at a profit.

Similarly, upon seeing a large sell order, sell short ahead of that, then cover the short trade after the price falls.

This might be compared to "shooting fish in a barrel", or "taking candy from a baby".

References:

Harvard: abstract

Money Science: Toxic Equity Trading Order Flow...

Economic Policy Journal: Here's a serious situation that could blow...

- FZ: Mother People, "We're Only in It for the Money".

"Down on the boulevard, they take it hard... they say it can't be won, the way the game is done..." JB

Update
Someone asked how could I do this. I must say I do not own the computers that clear the trades, so I can't see how I could do it, and it's not something that most ordinary people could do. If I had access to those computers... well, I suppose somebody does.

Update
I just found this
http://market-ticker.denninger.net/archives/1259-High-Frequency-Trading-Is-A-Scam.html
The key related paragraph:

"While markets are supposed to ensure transparency by showing orders to everyone simultaneously, a loophole in regulations allows marketplaces like Nasdaq to show traders some orders ahead of everyone else in exchange for a fee."

Further update
Goldman Sachs Has First Quarter With No Trading Loss. Quote: “It will reinforce the heads we win, tails you lose mentality that people think actually exists and promotes the concept of an unfair advantage,” said Douglas Ciocca, a managing director at Renaissance Financial Corp. in Leawood, Kansas, which oversees about $2 billion in assets including Goldman Sachs shares. “It’s too politically charged not to, how is that possible that they only make money?”

Further update (4 June 2010, 9 days after this write up)
Wall Street Journal just reported on the practice, saying "Some fast-moving computer-driven investment firms are getting an edge by trading on market data before it gets to other investors, according to market players and researchers who have studied the trading."