Class A airspace is a fairly straight forward type of airspace to understand, it covers the entire globe, from 18,000' msl or FL180 (flight level 180) up to and including FL600 (or 60,000' msl).
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Class A airspace is generally the airspace from 18,000 feet (~3.4 miles, 5.5 km) mean sea level (MSL) up to and including flight level (FL) 600 (~11.4 miles, 18.3 km), including the airspace overlying the waters within 12 nautical miles (NM) (~13.8 miles, 22.2 km) of the coast of the 48 contiguous states and Alaska.
Private pilots, however, are permitted to fly in every airspace class except for Class A, which requires an instrument rating. Private pilots who do have an instrument rating, however, are allowed to fly in Class A, but they cannot exceed 18,000 feet in altitude.
The biggest reason for flying at higher altitudes lies in fuel efficiency. The thin air creates less drag on the aircraft, which means the plane can use less fuel in order to maintain speed. Less wind resistance, more power, less effort, so to speak.
§ 103.23 Flight visibility and cloud clearance requirements.All operations in Class A, Class B, Class C, and Class D airspace or Class E airspace designated for an airport must receive prior ATC authorization as required in § 103.17 of this part.