Describe how the axis powers came to control much of europe but failed to conquer britain

They took it by storm. They developed and used the system of blietzkrieg warfare which was basically about using tanks and aircraft to quickly take as much land as possible before the opponents even had the time to react and it was successful for taking countries like Belgium and France, Poland, and parts of Russia.

They failed to take control of Britain because Britain was an island that couldn't be reached quickly by Tanks. They could only focus on bombing Britain to keep it in a bad condition but Britain had a strong air-fleet too as well as naval power so it was difficult to board a full attack on British soil which is why Britain wasn't occupied unlike France for example.