Divergence refers to a situation where factors move away from or are independent of others. With the MACD, it is a situation where price action and momentum are not acting together.
For instance, divergence can indicate a period where the price makes successively lower highs, but the MACD histogram shows a succession of higher lows. In this case, the highs are moving lower, and price momentum is slowing, foreshadowing a decline that eventually follows.
By averaging up their short, the trader eventually earns a handsome profit, as the price makes a sustained reversal after the final point of divergence.