Branches are the common in the overworld. They are incredibly useful in that they are necessary for making your first tools.
Branches are often found scattered in the overworld near trees. They are also commonly dropped when one cuts down a tree.
Branches can be used to make Crude Tools - this is the first tool you will need and possibly the most useful tool you have.
Branches can also be combined with Sharp Bones (found by skinning animals) to create spears, an excellent hunting weapon.
Lighting branches that are on the ground can also start fires - fires allow you to not die of low temperature and to not die of low sanity. They can also be used for cooking raw food.