I made a mistake while building an armature. Somehow a finger ended up attached to a backbone. Anyway, I am trying to reverse the mistake, but am not sure of how to move a bone from one armature (the backbone) to another (the arm).
A bit of clarification on terms: The individuals Bones are not Armatures. An Armature is a set of Bones that operate together. It must have at least one Bone, so when you create an Armature, you also create a Bone. Other Bones can then be added to that same Armature. Within the Armature, Bones can be children of other Bones, in order to create the hierarchies necessary to have the armature function normally. So as test-dr says, it seems likely you only need to re-parent your bones rather than move them to another Armature, which can’t be done in a simple fashion (the complicated fashion probably isn’t a good idea except in exceptional cases ).
If through some misunderstanding of the usual methods, you have actually created different Armatures for each portion of your rig (such as the backbone and the arm bone), then Join might be a reasonable way to do a workaround, but it has pitfalls like the root bone issue test-dr mentions.
In some cases multiple armatures for a rig are an efficient way to combine rig capabilities (some of my advanced rigs use three different armatures), but the more usual way is with a single armature containing all the necessary bones.