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."