The Bloodline of a player is very important; If the player has the potent blood of an ancient hero in his or her body, he or she can receive wonderous powers and abilities. If one desires to become a ruler, he or she must have this special blood (the character is said to be "blooded") in order to become an effective ruler. The blood is tied to the lands the character rules, making him or her a more able leader of his or her provinces.
The Birthright system also has a very innovative way of handling the costs and abilities of the rulers. There are a new form of "currency", Gold Bars, to handle the large costs of being a ruler, and a system of Regency Points, to handle the "finesse" a ruler has while ruling. There is also an admirable mass-combat system involving cards that represent whole units of troops that facilitates the battles that occur on the large-scale. There is also a very nice system of determing how outcomes of large battles can be determined easily.
Some other interesting aspects I liked: different racial modifiers, including modifiers for each human race; different racial stereotypes (specifically, that Elves and Humans don't get along instead of the Tolkien standby of Elves vs. Dwarves); different monsters, including the really cool Abominations; a "bigger" form of Magic for regents (the realm magic); and a whole different world with a developed history.
Personally, it's the only AD&D boxed set that has ever gotten my attention. I usually prefer some kind of homebrew games over a boxed set, which I often find very constricting for my method of GMing. I bought it and am very pleased with the purchase. I recommend it highly to anyone who wants to run a political campaign in a fantasy-adventure setting.
For a more complete description of the Birthright setting, check out the Birthright section at TSR's official homepage.