Plain English Meaning
Approaches into an airport that the FAA has officially designed and printed on charts, so any qualified pilot can fly them using the steps shown.
Full Definition
Instrument approach procedures that have been formally designed, flight-checked, and printed by the FAA (or equivalent authority) on official approach charts, making them available for use by any appropriately equipped and authorized aircraft. Each published approach specifies the navigation aids, fixes, courses, altitudes, descent profile, missed approach procedure, and required to fly the approach safely to a or airport.