I always thought it meant that the Lord's voice was so powerful that it broke the trees (like a shockwave), and made the mountains shake (like an earthquake). The verb that's translated here as "skip" can also be translated as "dance" if that helps, and there's another passage somewhere that speaks of mountains dancing, so I think of that as a common image. (Sorry--I can hear the song in my head, but I can't remember the context.)