The node point is where the natural harmonic is. For example, if you touch the string over the 12th fret. The node point is a small spot where the string is not actually vibrating, or at least isn't vibrating enough that when you touch the string there it doesn't mute it. What happens instead is you hear the parts the string has been split into.

I shouldn't try talking about wave physics 6am without any sleep. If any of that is screwed up someone correct me.