Information adapted from wikipedia
Parametric stereo works by taking the two mono streams that make up a stereo stream and combining them together to form a new single mono audio stream, but 2-3 kbit/s of side info (the parametric stereo) is also recorded. By having the parametric stereo side info along with the mono audio stream, the decoder (player) can approximate the original stereo.
Because only one real audio signal is sent, along with the negligible side info, a 24 kbit/s stereo stream of audio and a 24 kbit/s stream of audio with parametric stereo will be drastically different in quality. This can be modeled as:
12 kbit/s mono + 12 kbit/s mono = 24 kbit/s
But, with parametric stereo:
22 kbit/s mono + 2 kbit/s PS side info = 24 kbit/s
This makes the overall sound quality sound like a 22 kbit/s per channel piece of audio, rather than a 12 kbit/s piece of audio. That's 10 kbit/s more per channel, making the comparison more like:
24 kbit/s vs. 44 kbit/s
for the same amount of data.