"A better rhythmic pulse is produced if you relax left-hand pressure at these points ('). However, do not remove fingers from the strings. Also, if open strings are involved, mute them with the side of the right hand at the same instant that you relax left-hand pressure.", From 'Modern Method for Guitar' by William Leavitt.

Is this basically telling me to mute the strings then strum? How do I mute the strings with the side of my right hand (strumming hand)? I can't seem to mute and strum at the same time.
Im not entirely sure what all that means but it sounds like accenting your chords with your left hand, strum then release pressure but dont take your fingers off the strings, this causes the strings to mute, so instead of just a constant ringing chord every time you pluck it, you are adding a brief silence in between. It works very well for Palm Muted PowerChords to add that little something extra to an otherwise plain riff.

with the open strings, you cant release pressure to mute them so rest the side of your picking hand on the strings right at the bridge, just enough to dampen the sound, like palm muting position. Pluck your chord with an open string then rest your right hand on the strings to stop the sound.

make any sense?