Laymens answer, HE detergents are concertrated to work with smaller amounts of water which is how the newer Washing machines work. Smaller amounts of water and higher aggitation speeds. The HE detergent is formulated to have the same amount of detergent per water amount as regular detergent.
Your HE washer uses less water than a regular washer so HE detergent is made to compensate so you do not over soap you clothes, which does not rinse out and it does not create an over abundance of foam which can make your washer malfunction. Regular detergent can make your new HE washer actually think there is more water in the machine than there really is.
Washer manufacturers recommend that only HE detergents be used in their front-load and high-efficiency washers, and most will even recommend a particular brand of HE detergent. There is a good reason for using detergent that is specially formulated for these newer front-load washers. HE detergents are concentrated laundry detergents that are low-sudsing especially for use with low water high-efficiency washers.
If regular detergents were to be used in front-loading and high-efficiency washers, the presence of too many suds could 'confuse' washing cycles, cause delays and make proper rinsing of clothes difficult.