In short, "ne" is the negation word, but "pas" originally means "step" (or "a small step"). "Je ne mange pas." originally mean "I didn't eat a little". The form then evolve into standard way of expression negation.

This discussion leads me to this article: https://en.wikipedia.org/wiki/Jespersen%27s_Cycle.

Jespersen's Cycle describe the historical development of the expression of negation: from a simple pre-verbal marker of negation, through a discontinuous marker (elements both before and after the verb) and in some cases through subsequent loss of the original pre-verbal marker.

It's interesting to note that English underwent the similar transition (e.g. "I ate not today") but now it ended up back to the first stage.