The "Phoney War" references a period of time early in World War II where the public believed very little was happening. It lasted from September 1939 to April 1940.
The "Phoney War" period began immediately following Germany's blitzkrieg attack on Poland and the formal declaration of war by Britain and France. Public expectation was that similar attacks would immediately follow, but for some months neither side in the war seemed to be doing very much.
During this time, Germany was slowly occupying Poland. German submarines were sinking British boats, including the battleship HMS Royal Oak and the passenger liner Athenia (which was sunk by mistake). Britain was conducting air raids in Germany with propaganda leaflets instead of bombs and a form of martial law was instituted in Britain. Each side in the war established a blockade against the other.
The term may have been coined by Senator William Borah of the United States. This period of time was referred to as the "sitting war" by the Germans and the "twilight war" by Winston Churchill. It was later stated by German commander Alfred Jodi at the Nuremberg trials that Germany would have collapsed if France and Britain had attacked during this period.