Babel & Webpack
Babel
Gatsby uses Babel to allow you to utilize the newest Javascript features.
Babel is a free and open-source JavaScript compiler that is mainly used to convert ECMAScript 2015+ code into a backwards compatible version of JavaScript that can be run by older JavaScript engines. Babel is popular tool for using the newest features of the JavaScript programming language.
Babel will compile your code down during the Gatsby build process so you don't have to worry about cross browser support, you just write your JS and Babel will make sure it works.
You do have the ability to customize the Babel config within Gatsby, but the defaults are typically a good starting spot.
Webpack
Gatsby uses Webpack to bundle all your JS together at build time.
Webpack is an open-source JavaScript module bundler. It is a module bundler primarily for JavaScript, but it can transform front-end assets like HTML, CSS, and images if the corresponding loaders are included. Webpack takes modules with dependencies and generates static assets representing those modules.
Gatsby comes with it's own Webpack config but gives you the ability to override it. Webpack configuration has taken the sanity from many brave developers, so not having to deal with setting up the default conifiguration is a huge time (and sanity) saver.