Chances are when you’re listening to Pandora on your stereo, you just plug in your phone and start playing. However, if you have Pandora One, you get significantly higher quality music if you use your computer instead.
Pandora’s free stream is of comparable quality between devices (64kbps AAC+ vs 128kbps MP3), but if you upgrade to Pandora One, your computer is the best device to listen from. From Pandora’s help page:
Pandora on the Web plays 64k AAC+ for free listeners and 192kbps for Pandora One subscribers. All in-home devices play 128kbps audio, and mobile devices receive a variety of different rates depending on the capability of the device and the network they are on, but never more than 64k AAC+.
None of these are as good as listening to the music on a CD, of course, but listening to a 192kbps MP3 instead of a 64kbps AAC+ file should produce a noticeable boost in sound quality (though your ears may differ). Try it out for yourself and see — just make sure you’ve turned on high quality audio in Pandora’s settings.