Front running happens when a broker acts on information they've gotten that no one else has yet. It's illegal, of course, but it's such a lucrative practice that people just can't help themselves.
Example
Giant Mutual Fund X wants to sell 50 million shares of Exxon. Their trusted Giant Broker Y is happy to handle the order. In a fair world, Giant Broker Y would solicit bids for small blocks of shares so as not to affect the price of the stock (Giant Broker Y knows, after all, that when huge orders of stocks are filled, it can affect the stock price).
But what if Giant Broker Y has its own funds, which it manages for itself on behalf of the partners of its firm? And what if Giant Broker Y could make $2 a share on 50 million shares by using options in a transaction which it executes ahead of Giant Mutual Fund X's order?
As with many things in life, the problem is the money. If "all they took" was a commission for being an agent on behalf of Giant Mutual Fund X, they might make 5 cents a share or $2.5 million. Hmm... $100 million vs. $2.5 million... How much is a trader's soul worth?