A string damper mutes open strings of a guitar when not in use. Jennifer Batten (who IS magically shredderiffic) does a lot of two handed tapping up and down the fretboard. So, say for instance Jennifer does a two handed tapping run on the high E. Slap the damper down, and if she happens to bump the B string while going up and down the neck it won't make a bone jarring note pop out and mess up a perfectly good solo. Fretted notes above the damper are unaffected.
Michael Angelo Batio (another shredder) has 'em on some of his guitars, too.
I used to take a sock and tie it around the first fret when practicing speed runs when I was younger as well for the same effect (although definitely not as cool looking).
There was a thread a while back that had some amazing girl guitar players on it here recently, but I don't think Batten was mentioned.