There were two major strengths that the Axis Powers enjoyed in WWII. (I am speaking mainly of Germany and Japan here.) These were that A) they were much more ready to fight and B) they had more experience and better war plans than the Allies originally did.
When WWII broke out, the Germans and Japanese were ready to fight where the Allies were not. The Axis had been planning the war and were naturally more prepared for it than the Allies. The Germans had much better plans for the war (the new tactic of blitzkrieg) than the Allies had. The Japanese were much more experienced at fighting because of their recent experience in China.
It is also worth mentioning that the Axis had better weapons in some significant ways. For example, both the Germans and Japanese had better airplanes at first than the Allies did.