What enabled the Allies to win the Battle of the Atlantic?

The Battle of
the Atlantic occurred between
German U-Boats (submarines) and the surface American and British
Fleets. 
Between 1941, when the US entered the Second World War, and early 1943, the German
subs
contained US shipping to Britain with traditional submarine tactics that
had been developed
during World War I.  The traditional counter-strategy was
for the Merchant Marine, which was
transporting war materiel, to travel in
convoys, made up of navy escorts (battleships and
destroyers) to accompany
the transport ships, the US covering from its coast to Iceland, and the

British covering from Iceland to its coast.  This strategy worked better than single
ships
crossing the Atlantic, but losses continued to mount.   Admiral Karl
Doenitz (1891-1980) devised
the concept of the "Wolfpack," to amass
underwater firepower by grouping numbers of
German subs together to
simultaneously attack the convoys.  By producing subs in large numbers,
he
believed they could contain the whole of the Allied War effort, and for a time, he was
proven
right!  Allied shipping began to incur huge losses -- so much so that
it became known in the
German Submarine fleet as the "Happy Time," as very
few German subs were lost, and the
monthly tonnage of Allied shipping sunk
continued to increase ominously.  However, Allied
technological advances
began to destroy the wolfpacks -- Great Britain shared its ASDIC system

(Anti-Submarine Detection Investigation Committee) which the US termed SONAR (SOund,
NAvigation
and Ranging) which enabled both surface fleets to track and
destroy subs more efficiently.  The
US began a plan of air escort, with
aircraft equipped with antisubmarine bombs which could put
the sub on
defensive before it could acquire a ship and launch its torpedoes.  Finally, the
US
developed an forward throwing offensive weapon for ships known as the
"hedgehog,"
which could quickly saturate an area with depth charges and
increase the chances of a hit on a
sub.  These measures began to destroy more
German subs and crews than could be replaced, and by
1943, the tide had
literally turned in favor of the Allies.  By war's end, Germany had 30,000

casualties of the 40,000 underwater sailors that comprised the submariner fleet. Winning
the
Battle of the Atlantic was critical for the Allied war effort; once the
Atlantic was under
Allied control, the full industrial output of the US could
be shipped to Britain and brought to
bear against a conquered Europe. 
Stockpiling supplies began in earnest in England; the invasion
of Europe
(D-Day) followed within a year.

Two excellent references on
this
topic are the movie Das Boot ("The Boat") and the
World
at War video series, episode 14, entitled
"Wolfpack."