Crowns:
You can earn Crowns on each level depending on whether you are the best out of all your friends, in terms of performance, on that particular level. If you are, you will receive a golden crown. If you are second, you are given a smaller, silver crown, while third place amongst your friends earns you a bronze crown. This is an extra incentive to keep playing and to try to beat your friends scores.
Bird-O-Matic:
The Bird-O-Matic is a tool that you can use to customize your game's avatar. You can add items such as hats and other accessories, and generally make a bird that fits your personality, and makes it stand out among your friends.
Angry Birds Shop:
The Angry Birds Shop is an option in the menu which lets you buy power-ups to assist you in your quest through the game, or to give to other players as gifts. You can purchase all of the items detailed below in the Power-Ups section, as well as the Mighty Eagle, if you've earned the chance to use it, and an All-in-One Bundle.
This bundle essentially includes all of the power-ups in one convenient package, and is useful for priming yourself for any potentially tricky situations. Everything you can by in the shop costs Facebook Credits, though you can earn most of it through playing the game's levels.