Server-side JavaScript

The first incarnations of JavaScript lived in browsers. But this is just the context. It defines what you can do with the language, but it doesn't say much about what the language itself can do. JavaScript is a "complete" language: you can use it in many contexts and achieve everything with it you can achieve with any other "complete" language.
Node.js really is just another context: it allows you to run JavaScript code in the backend, outside a browser.
In order to execute the JavaScript you intend to run in the backend, it needs to be interpreted and, well, executed. This is what Node.js does, by making use of Google's V8 VM, the same runtime environment for JavaScript that Google Chrome uses.