Palm mutes are important as they give more expression to both your chords and solos. To do a palm mute, place your palm near the point where it meets the bridge and strum/pluck. Try it out several times to find your 'sweet spot' - it depends on the size of your palm, the type of bridge, etc.
This video demonstrates several practical applications of palm mutes. You can use it to make the groove stronger by muting the bass notes of chords, or build up to a climax. You can also use it to give more expression to your soloing. Read here for more, including some close-up pictures on positioning your palm.