Plain English Meaning
The high-altitude airspace where every flight has to be on instruments and talking to controllers. You cannot fly through it under visual rules, no matter how clear the weather is.
Full Definition
The block of U.S. airspace from 18,000 feet MSL up to and including flight level 600 (60,000 feet), plus the airspace overlying the waters within 12 nautical miles of the U.S. coast. All flight in Class A airspace must be conducted under Instrument Flight Rules (IFR), and pilots must hold an instrument rating, file an IFR flight plan, and be in contact with Air Traffic Control.