Here, finally, must certainly be the last word on Angry Birds. Certified Human Factors Engineering Professional Charles L. Mauro has done an exhaustive report called "A Cognitive Teardown of Angry Birds," in which he breaks down, piece by ever-lovin' piece, the throw-birds-at-pigs game and just what it does to users and their experiences.
The whole thing is quite interesting if you're into user experience design, but the gist is that Angry Birds fits extremely well within our brains' "mental model" of what the game should be. Not only is that bird-tossing physics engine easily calculated into our cranium, but the game's bite-sized levels (which you can scroll across to re-check at any time) also play into our short-term memory programming as well.
And finally, Angry Birds nails down the visual experience by being both simple enough for almost anyone to understand, but just complicated enough to remember in an iconic way (so much so that the characters in the game have been turned into cakes, costumes, and even, um, bras. What Angry Birds did is no secret (and lots of other games have aped its look and aesthetics since -- that "star rating on tons of levels" feature is now an iOS staple), but Mauro has done an excellent job really breaking down point by point why this game is so astoundingly successful on a cognitive level.