Bones are resources that are primarily obtained from killing Monsters and which can be used to create Bonemeal required for Farming certain crops, to Craft Arrows, or as Brewing ingredients for Fertilize Soil Potions.
Besides regular bones, there are also Ashes, Ice Bones, Zombie Bones, Blood Bones, and Fish Bones, which can also be used to create Bonemeal. Skeletons are the best kind of monsters to kill for regular bones. Additionally, the Bone Amulet and the Bone Ring will give double (triple if you use both) bone drops for all monsters dropping regular bones.