In a foot race, a front-runner takes off ahead of the pack and hopes to build an insurmountable lead. In the stock market, it's someone who takes off ahead the same way but then tries to convince the rest of the pack that he or she is not really a front-runner.
Such is the convoluted world of Wall Street trading, where competitors will go to extreme lengths to try to outwit the competition.
In conventional terms, front running is something that happens within a firm: A trader gets word that a customer is interested in purchasing a big block of a company's shares, and that trader will purchase shares for his individual account before executing the customer's order. When the customer's purchase gets executed, the price rises and the trader pockets the difference between the new price and what he paid.
However, that definition, or at least the term's connotation, has changed some recently.