Why was Battle of Britain important?
Because if the British air force had not been able to overcome the German attacks, Germany might have gone on to mount an invasion of Britain, having established air superiority. The British Navy was superior to the German, but without air cover it would have been very vulnerable. The US was neutral and not in a position to help much anyway, being a long way off and not geared up for war. If Britain had been occupied by Germany, the US would never have been able to mount an invasion of Europe.
