What "Mastered for iTunes" does
Just a quick summary what it does, and why it improves the sound (unless you start with rubbish music, where nothing will help):
First, it encodes from 24/96 masters directly to AAC, instead of going 24/96 -> 16/44.1 -> AAC. There isn't much loss in the first step, but there is some. And the loss is noise, which is harder to compress than music, so not having to compress that noise should make the AAC a little bit better.
Second, it avoids "clipping": Clipping happens when your music goes above the limits, and sounds awful. Many record companies convert music to CDs so that it is just short of clipping, using 99.9% of the available space. But lossy compression like AAC won't reproduce the music exactly, so sometimes the AAC might go to 100.1% and get clipped. "Mastered for iTunes" gives the recording studio tools where they can look for clipping in the AAC file, so they stay about further away from the limits, just enough that the conversion to AAC will not give clipped results.
There were some reports where "Mastered for iTunes" didn't sound any better, and it turned out the music was already clipped before it got anywhere near "Mastered for iTunes". In that case the damage is already done, there is nothing you can do.