ADR stands for "Advanced Dining Reservation" and you will need them for the four Table Service credits you will receive in your Free Dining plan.
I'd read up on the Dining Plan and general restaurant boards here if I were you, but basically, the most popular table service restaurants will require an ADR to eat there.
TS credits can be used for breakfast, lunch or dinner. In exchange for each credit, you either get a buffet or family style meal, or an entree and dessert at the a la carte restaurants.
With a two year-old, I'd make sure to book at least one character meal (maybe two). Chef Mickey's is great, but hard to get a decent time ADR for. The Crystal Palace has always been excellent for us, but DH balks at eating there because he can't get a cocktail there. :rolleyes