The "highest delta expiration date" is when the largest amount of delta (directional exposure) expires in the underlying stock. 

Options market makers may have a large hedge position which they will remove following this date. Therefore, if large amounts of delta far out-of-the-money are on track to expire, then this can create strong directional flows influencing market movement. 

If dealers have large amounts of negative deltas trapped far out-of-the-money, then this can create bearish flows if they are set to expire soon, with the logic being that this directional positioning would need to be replaced. And vice versa, if dealers have substantial bullish deltas on their books about to expire, then this can create bullish flows because they may begin to replace them with heavy buying in the underlying.