What happens if you connect a short copper wire to both the positive and negative terminals of a battery and why?

The wire will get hot, the temperature it gets up to will depend on the ampere of the battery and size of wire. The wire can get hot enough to causes burns or start a fire if the battery is large enough. Why this happens is because you have shorted the battery out. The power comes out of the positive post and back in the negative post. When you short it out the power can flow from one post to the other very quickly causing the short to get hot, due to the amount of flow.