Palm muting is where you place your strumming hand on the strings while you're strumming. This gives a shorter and more suspenseful sound.
It's used a lot in rock, metal and acoustic music.
Placement of your strumming hand is crucial. Move your strumming hand back so it's close to the bridge. Don't press down on the strings. Let the weight of your hand provide the necessary dampening of the strings.
It's also worth mentioning that when you're palm muting you can't strum all 6 strings. Playing the first 3 or 4 strings is fine.
In TAB palm muting is written as pm (palm muted) and has a dotted line like this:
You then palm mute for as long as the line covers the TAB.
There's 2 sheets of TAB for these 6 examples.