Natural harmonics are overtones you can get from the string's full length, that is from bridge to nut. The technique for playing pinch harmonics is sometimes called the "movable nut" because that's what your left hand do. When you fret a note, say the C on the G string, 5th fret, the length of the string is shortened. Your left hand finger act as if you move the nut to that position, so the whole harmonics relationship along the string is transposed by that interval. But now your left hand is busy, so how do you touch the string in the different points (nodes) for getting the harmonics? Using your right thumb. How pluck the strings then? With your right index and/or middle fingers.
If you don't know how harmonics work on a string, check
this thread. I think it's well explained there.
This one may also help.