Jest isn't primarily designed for React. It has a lot of built in feature for making testing React components easier. But it's a generic Javascript test runner and framework
Yep - the main thing that Jest gives out of the box is jsdom, so allows for dom based testing without needing phantom (or more modern now, headless browser).
I also find it's faster and has better features than Mocha (for instance, coverage out of the box).
I also find it's faster and has better features than Mocha (for instance, coverage out of the box).