Vagus Nerve... What?

Compassion and the Vagus nerve... this is an assignment that I've been avoiding for... 3 months now. I've read the articles many times and they still don't make sense. I feel like the squirrel from ice age chasing it's acorn! Sometimes I get it but only for a short while before it escapes my grasp and I find myself chasing it again. By it I mean understanding the vagus nerve and how it relates to compassion.
Sure it makes sense that it would be related. After all the vagus nerve does innervate the heart, lungs and stomach (along with other things but these are the main organs) all of which are organs that come into play when emotions are involved. Scared - rate of breath increases, nervous - rate of breath increases, heart broken - heart aches... but then they go an throw in the polyvagal theory and other shit in there that has me really freaking confused!
Ah heck! I should stop blogging and keep wracking my brain. So far I've been working on this assignment for two hours tonight and I've managed to semi answer one question. I still don't think I'm on the right track but hell.