Front Running is the criminal practice of executing trades/transactions based on non-public, insider knowledge of incoming private demands.
In traditional finance, front running happens in a schema similar to what follows: Alice is buying $1B worth of CTB. She executes the order through her broker. It is Friday & CTB is trading at $100. Her broker will put in her order for CTB @ $100 each on Monday. As the broker goes in to make the purchase, he realizes that there is an opportunity to arbitrage out a few points gain. So he buys $1,000,000,000 worth of CTB on friday for an average of $99.45. He knows that once that order size hits the market the asset will rally to ~$115 each. So, as Monday comes around, the broker puts in the $1,000,000,000 order and sells HIS shares to Alice. Making a guaranteed & illegal $0.55 a share ($5,500,000) without any risk.
Within the context of cryptocurrency and blockchain, front running play the same role under slightly different parameters. Nodes that run Decentralized exchange software (DEX’s) receive information about incoming transactions locally before they are executed on-chain. Once a node see that somebody put in an order for 100,000 ZRX @ $1 and ZRX is trading @ $0.985, that node can delay the transaction from hitting the chain, buy as much ZRX as possible ~$0.985 then place their assets on the orderbook @ the ~$1 and execute the incoming buy for a $1 ZRX. The node risk free profits $0.015 per ZRX ($1,500 for manipulating the orderbook and exchange operations)