Rovio announced that Angry Birds Action players should open up the game during the end credits of the movie. Completely the opposite of what those ads before the movie telling you to put your "bright little screens" away tell you to do.
During the end credits of The Angry Birds Movie, a special inaudible sound has been implemented. The game will listen to the sound and automatically unlock special levels and new content within the game.
Rovio has uploaded a video to YouTube explaining the technology, which can be watched in the reply below. Angry Birds Action can be downloaded in the iTunes App Store for free.