Falcons are neutral mobs. They can fly, and can be found near mountain biomes. When killed, it will drop a falcon egg, or feathers. When feeding raw fish to two falcons, they will breed and create a falcon chick. If a Falcon lives long enough it will get bigger, and bigger. They can be fed porkchops to be tamed. You can use them to assist you in fighting.
Falcons will just roam around, flying on the sky, finding water to land on. When you hurt a falcon, they will attack back. Also, if its big enough it will swoop down and grab pigs, cows, etc. Sometimes, it might even grab the player. It will more-in-likely fail and will not keep you up.