Couldn't find a suitable answer in the FAQ, so asked it. I used to spend a lot of time reading about WW2, although now I'm doing my degree I have less time. I'm more or less familiar with most major events from 1919 onwards, including most of the major engagements and campaigns of the war, so feel free to use more specific references beyond the ELI5 level.
There is not definitive answer to what exactly the Axis Powers did wrong to lose the war, but much of it has to do with two major events in 1941.
By 1940, Germany had knocked Poland and France out of the war. The Battle of Britain was the Germany attempt to either prep for a land invasion of Britain or force Britain to the bargaining table. However, it failed in both of these goals.
So in 1941, knowing the Britain had not been defeated, Hitler still felt that they were not a threat to continental Europe anymore. It was at this point that the planning and execution of the invasion of the Soviet Union began.
While the Soviet Union had recently fared poorly in the Winter War with Finland and suffer from several military purges, it still possessed the vast amounts of men and resource to draw upon. In fact, for the remainder of the war, Germany would expended the majority of its resources in fighting the Soviet Union, not the Western Allies.
The second event was the attack on Pearl Harbor and Japan's declaration of war on the United States. At this point, war with Japan did not necessarily mean war with Germany for the US. However, Hitler declared war on the US anyway.
As a result of this, by the end of 1941, Nazi Germany was at war with the richest country in the world (the United States), and the largest military in the world (Soviet Union).