How to deploy vue-webpack app using production build + nginx

I have an application built using the vue-webpack boilerplate. Obviously it all works fine in dev, production is where I'm confused.

I have a DigitalOcean droplet all set up with Nginx as a proxy. Also working well. Here's the problem: I have no clue what to do with the npm run build command. I know it builds it all and does all the great webpack stuff that's buried in there. But where's the server? Do I just set the nginx root in the server block to ./dist/index.html or whatever?

Shouldn't there be a server running? Or do I just run the dev-server with a couple env variables declared? Really confused as to how to take advantage of the production build.

via Will Carron