What is the importance of the Battle of Midway?

The Battle of Midway was important in a couple of ways. 
The largest importance the battle held was that it repelled the Japanese from advancing
against the United States.  Following the success of Pearl Harbor, the Japanese military
sought to make another advance that would permanently cripple the United States Navy and
move them back to California, giving control of the Pacific Islands to the Japanese and
allowing them significant advantage against the United States.  The Japanese forces
failed to calculate that weakened is not the same as defeated.  American forces utilized
intelligence and stealth in a much more effective manner than did the surprise element
of Pearl Harbor.  Led by the strategically minded Admiral Chester Nimitz, U.S. Naval
force was able to design an attack strategy that baited the Japanese vessels into a
conflict that they were not expecting and for which they were not prepared.  Along these
lines, the losses that the Japanese suffered were immense, losing significant aircraft
and naval vessels as well as some of their best pilots.  From a momentum point of view,
the battle was important in that it killed off Japanese advance and shifted the momentum
to the American forces who were now able to repel the Japanese and could themselves
advance further into the Pacific Rim.  Less than a year removed from Pearl Harbor, the
Americans proved themselves to be the equal of the Japanese in the Battle of
Midway.