My interpretation was: In their previous lives in ancient China, they got these stones put in them that 1) make them physically invulnerable and 2) bind them together for all eternity.

It's unclear to me, however, why in this particular incarnation they didn't start being physically invulnerable until during/after the epic final battle, and whether Dean's powers were supposed to be because of the stones. I feel like, given all the other stuff she had going on, she could've taken the time to handwave that stuff.