Watch the Sixths and Thirds online guitar lesson by Angus Clark from Hard Rock Survival Guide: Rhythm
This lesson is about "Breaking up the Chord", either by playing selective strings from a big chord, or by choosing just an interval like a sixth or a third in order to imply an entire chord. In the case of selective string playing we're using damping and right hand muting to create the sound of two parts going on at once.
On the interval side, there are a ton of different uses for sixths and thirds in hard rock. You should just be able to recognize what chord you are implying, or what scale you are working out of very quickly. One bonus of utilizing sixths and thirds is that it allows you to come up with twin guitar harmony parts, which can be equally effective in rhythm playing as they are in lead playing. Just look at Judas Priest, Iron Maiden, Avenged Sevenfold, and Bullet for My Valentine.