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What does "Fall Gelb" mean?
Short answer
It means "Case Yellow": the name of the German plan to invade the Netherlands and France. It is also known as the Manstein Plan, after its planner, Field Marshal Erich von Manstein, and as Operation Sichelschnitt, "sickle cut."

"Case Yellow"
Fall Gelb, "Case Yellow," was the name of the plan for the invasion of the Netherlands and France. It constituted the first phase of the German offensive and is also known as the Manstein Plan, after Field Marshal Erich von Manstein, who devised it. Another name used was Operation Sichelschnitt, "sickle cut." Hitler had long planned to avoid a two-front war, although he was aware of the risk.
A code name predating the campaign
The German pre-war code name for the campaign plans in the Netherlands was Aufmarschanweisung No. 1, Fall Gelb. The plan envisaged an advance through central Belgium. There were successive amendments: Aufmarschanweisung No. 3, Fall Gelb, of 30 January, and a later one, Aufmarschanweisung No. 4, Fall Gelb, which lacked, to Guderian's displeasure, an element of the earlier plan. On 24 February the main German effort shifted south, to the Ardennes.
From execution to Fall Rot
On 10 May 1940, five Panzer divisions of Panzergruppe von Kleist began their advance through the Ardennes region. Army Group B was assigned almost 2,000 combat aircraft, and Army Groups A and C more than 3,000, an air force almost twice the size of the Allied one. After the evacuation of Dunkirk, the Fall Rot (Case Red) plan was to finish off the French and the British.
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