The amplifier is meant to work with the factory head unit to amplify the signal going to the speakers. It works well in the stock system, because that's the way it was engineered, but as soon as you change out the head unit, the factory amp doesn't work as well. The reason for this is that the aftermarket head units come with built in amplifiers, and the factory amp restricts the already-amplified signal, causing distortion.
If you have an aftermarket head unit, and are having sound quality issues, the first thing I would try is the amp bypass. It's less than $20 and will likely fix your issue.