After the end of World War II in Europe on May 8, 1945, the former nation of Nazi Germany was occupied by the Allied Powers. In order to manage administrative, political and logistical complications the country was divided up into Zones, with each Zone managed by a different Allied power. As a result, there were four major Zones - the U.S. Zone, the British Zone, the French Zone and the Soviet Zone. Berlin, as the capital, was itself divided into sectors (hence the famous sign at Checkpoint Charlie, "You are now leaving the American Sector").
Within each Zone, the problem of the economy and currency was handled differently, although the broadest differences were between the Soviet Zone and those of the Western allies. The reasons for this were variegated, but several stand out. For one, the Soviet Union was intent on punishing Germany for the war and ensuring it could no longer pose a threat by stripping it of economic as well as military assets, and in addition deliberately crippling its economy. The Western Allies, however, were intent on rebuilding Germany as an economic power in order to avoid what they saw as a possible repeat of the conditions imposed by the Treaty of Versailles after World War I. The crushing economic burden that treaty placed on Germany was seen as a major cause of the Second World War.
All of the various occupying powers began to print their own currency for use inside Germany. This was not only for use by the citizens of Germany, but mostly was used to pay the occupying military personnel - thus encouraging them to spend their pay locally and to stimulate the local economy. At the time, there were old Reichsmarks in circulation, as well as AMC marks (Allied Military Currency) as well as various local forms of exchange.
At the Potsdam conference in 1945, the split between the Soviet Union and the Western allies had become apparent. As one result, the Western governments began to work on how to repair Germany's economy without the input of the Soviet Union. By mid-1946, the agreements on transfers of dismantled Germany factory machinery as well as on the deportation of German citizens across zone boundaries had begun to break down. The U.S. and the U.K. had guaranteed to send a percentage of all captured German machinery eastward in exchange for agricultural goods intended to feed the refugees that the Soviet armies had pushed west, as well as repay them for their confiscated goods. The U.S.S.R. halted those deliveries of agricultural goods in mid-1946, causing the Western Allies to in turn stop sending further equipment eastward, retaining it for use in their own Zones.
Finally, on January 1, 1947, the U.S. and U.K. announced that they had merged their Zones of Responsibility economically in order to simplify the situation vis-a-vis the Soviet Zone and, as well, to counter the increasing obstructionism of the French Zone. The French had been encouraging local autonomy for the historic German states within its Zone, while preventing any central coordinating body from forming, in order to encourage Germany's breakup into sovereign, small, squabbling powers - in France's view, a much more desirable outcome on their historically fractious northern border than a resurgent and unified Germany.
The U.S. and U.K. named their merged zones the 'Bizone', and various people began jokingly referring to it as a nation with the proper name 'Bizonia'. Its formation, which despite the claims of the U.S. and U.K. also included a political centralization agenda, caused the U.S.S.R. to halt further cooperation. The U.S. and U.K. would continue to secretly create a new currency for the Bizone, naming it the 'Deutsche Mark'1 and in a coordinated surprise action release it across the Bizone simultaneously with limited exchangeability for the old AMC Mark and Reichsmark. This was done partially in response to the Soviets using the plates for the AMC marks given them by the U.S. to print massive amounts of inflationary fiat money inside the Soviet Zone, both to pay for their own supplies and to intentionally destabilize the currency of Germany as part of their own agenda. The situation would continue to worsen, and would result in the Berlin Blockade of 1947. Eventually, the Bizone (with the eventual addition of the French zone, briefly turning it into 'Trizonesia') would form the nucleus of the 20th century nation the Federal Republic of Germany. The conflict between the Allies continued and grew, and became what we now call the Cold War.
1 - Thanks to realplayer for the correction!