What's an "altitude engine"?
An altitude engine is a type of engine that uses a turbocharger (and less often, a supercharger) to generate sea-level pressure in its intake manifold, up to its critical altitude, at which point power will start to fall off. 

Non-altitude engines will lose power as they climb because the ambient air pressure drops off at a rate of about 1" Hg per 1,000 ft of altitude (up to 10,000ft).

The altitude engine allows aircraft to fly at higher altitudes at full power, and increases the aircraft's speed and efficiency, because true airspeed increases with altitude. It also allows an aircraft under IFR to fly at higher MEAs or under VFR over higher terrain, and allows the pilot to choose a favorable altitude for weather.

The first kind of altitude engine is called a turbocharged engine, which can generate more intake manifold pressure than at sea level. For example, a Mooney Bravo M20M can generate 36" of manifold pressure, and can generate at least 30" of manifold pressure up to its critical altitude of 22,000ft.

The other kind of altitude engine is called a turbo-normalizer, which develops a maximum of sea level pressure: 30”Hg or 1 Bar. These engines will perform as well at altitude (up to their critical altitude) as they do at sea level. 

A turbo-normalized engine is considered less taxing on the engine than a turbocharged engine because the former doesn't develop above sea-level pressure or high turbine-inlet temperatures. The turbo-normalized engine is also easier to fly than a turbocharged engine, since it never develops more power than would be developed at sea level.

All altitude engines also typically have a controllable-pitch prop, and develop more than 200 horsepower, so they would require both a complex aircraft endorsement and a high-performance endorsement. See 14 CFR Part 61.31.