To be very clear, the man page is claiming that Apple's
implementation of the AAC codec [the encoder specifically] is superior to other
implementations of AAC encoding; not that AAC is superior to other audio codecs.
If you're wondering how one implementation of an audio codec could be superior to others — mostly, it's because any lossy audio codec has an encoding phase called "psychoacoustic compression", where each implementation of the codec is free to do whatever it likes to "simplify" the waveform in some way (most easily pictured: by taking a Discrete Cosine Transform of the waveform, and then quantizing / convoluting some parts of the frequency space. Like what JPEG does to discard information from the chroma channels.)
IIRC, rather than blunt-force quantization, Apple's AAC encoding does clever things (akin to the instrument separation done to audio in Melodyne) to split the waveform into "features", and then discards information in such a way that the features' separability is maintained (i.e. it doesn't become harder to "pick out" any given "sound" from the audio.)