E|------------- B|------5x----- G|------------- D|------------- A|------------- E|-------------
This example means that the B string is played at the 5th fret and then the finger is lightly released in order to stop the sound as soon as possible. It gives a very sharp and short burst of sound.
These are frequently employed in Jazz and Blues.
String muting can be applied to a whole chord being sounded. The right hand rests on the bridge of the guitar and just barely touches all the strings. The position has to adjusted on a trial and error basis so as to make sure that some sound is produced on strumming, but that is muffled simultaneously.
Again, playing normally with the right hand, one may also mute the strings with the left hand. The chord is sounded and just like string muting, the left hand is gently released to muffle the strings. The sound produced is different when using left or right hand.
Palm muting is very common in grunge and metal.
Here's a free video explaining the technique and showing it in practice:
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