During warmup, the engine is runs in a preset rich condition which results in a lot of unburned hydrocarbons exiting the cylinders. The air pump provides the additional oxygen needed by the converter to convert the hydrocarbons to harmless carbon dioxide and water.
Once the car is warmed up the O2 sensor comes on-line and determines how the mixture is regulated. At this point the mixture is considerably leaner and pretty much optimized for combustion and converter efficiency by the O2 sensor, and the additional oxygen from the air pump is not needed.
95 E320 Cabriolet, 131K