What is the largest nerve of the entire body?
Please describe its function.

The sciatic nerve.

Sciatic Nerve (http://www.sciatica-pain.org/sciatic-nerve.html)

I thought it was the vega nerve which runs up and down the digestive tract.

The sciatic nerve is correct.

You can read here for it's function Rolcam.

Sciatica and the Sciatic Nerve (http://www.spine-health.com/conditions/sciatica/sciatica-and-sciatic-nerve)