ADR stands for Advance Dining Reservation. That's a term Disney used for awhile. Right now they seem to be merely using the term "reservation."
However, it's not a reservation in the true sense of the word. Making one won't guarantee a table being held open for you. What it means is that when you check into the restaurant, you will be given the next available table that will accommodate your party, cutting down on your wait time.
You can make an ADR for any Disney restaurant, not just character meals. There are a few restaurants at Downtown Disney that are not owned or run by Disney for which you cannot make reservations through Disney, but for other on-property restaurants, you can make reservations on the Disney dining line, (407) WDW-DINE, up to 90 days before you wish to dine there.