mp3s are a lossy format. they do not have the same quality as the cd that you OWN and ripped. copying mp3 to mp3 to mp3 does not cause a deterioration sound quality. you're thinking of the principle of analog dubbing. if you copied a copy of a copy of a VHS tape for example, the result would be very poor.
what Da_Taxman was saying in the second part of his post was that when you burn a cd there will always be errors on the disc. they will not affect sound quality, nor will they affect the play (unless there are many errors then they will cause skipping or freezing). things that affect error rates are speed of burn, firmware in the burner, model of the drive, and quality of media. these errors will not affect sound quality, but MAY affect data integrity. if you tried to rip a cd 6 months from now that you burned too fast on poor quality media, you may not be able to retrieve all of the data even though the files may still play in a cd player.