Plain English Meaning
The airspeeds a pilot is aiming for at each stage of the flight. Different parts of the flight call for different speeds, and 'desired airspeeds' simply means the ones the pilot has chosen to fly at that moment.
Full Definition
The specific target airspeeds a pilot intends to maintain for a given phase of instrument flight, such as climb, cruise, holding, approach, or landing. These target speeds are determined by the aircraft's performance data, the maneuver being flown, and any operational or regulatory requirements applicable to that phase.