The lower right picture gives a pretty good image of what's going on - there are flimsy houses full of pigs, and you need to fling (angry) birds at those houses, which will bring them crashing down (no problem there, as they don't have nails or screws, as the home inspector correctly observes), thus killing the pigs. Once all pigs are killed, you advance to the next level containing bigger houses, more pigs, etc.
In case you didn't know yet... Angry Birds is the most popular game on the iPhone and iPad and one of the most successful apps in Apple's App Store. It has been sold tens of millions of times. The iPhone version costs € 0,79 here, I guess it costs $ 0,99 in the US.