I've created a quick React JSX example 'Hello World' project ( https://hyperdev.com/#!/project/glaze-dagger ) that you can take a look at.
There's some useful background about what a package.json file does on the npm site ( https://docs.npmjs.com/getting-started/using-a-package.json ), but it essentially allows you to specify what packages you want to use in your project, amongst other things.
In the case of the React JSX example, if you look at the package.json file you can see we're including express and the express jsx transform packages in the dependencies section. So if you're told to add it to your package.json, typically they just mean to add whatever package they're referring to there. We make it easy to do that in HyperDev by embedding npm. So if you search for the package you want from the 'Add package' drop-down at the top of the editor window when viewing the package.json file, it'll automatically add the required line to your package file.
We also have an implementation of the main React tutorial project that you might want to follow to understand some of the core concepts about how React works: https://hyperdev.com/#!/project/shade-king. If you remix it, then you can play around with it for yourself.