There is a FAQ about the
DDP at the top of the page. Basically, if you're staying onsite and buying at least 1 day of park tickets, you can buy the dining plan for each person in your room. For each night that you're booked at the hotel, you get 1 snack, 1 table service meal (appetizer, entree, dessert, drink, tax, tip included), and 1 counter service meal (entree, dessert, drink, tax included plus tip if applicable).
It's a fairly good deal, considering the amt of food you get.
The DDE is a membership card, moreless, that is only available to Florida residents and those that hold annual passes to WDW. It gives a % off their dining and alcoholic drinks at most places around WDW. I believe it's 20% off. I am unsure of what the initial cost is, honestly, since I don't qualify for it.
For many, the DDE is a better choice because they don't want to buy park tickets to get the DDP (they already hvae annual pass) or they live in FL and take frequent trips and don't necessarily want to buy rack rate hotel rooms.
But for most of us, we don't qualify for the DDE.
HOpe that helps some - feel free to ask more questions!