Node.js is a runtime environment.
Think of it this way—you can have a webpage with JavaScript code on your computer, or on a server, or wherever. Still, it doesn’t do anything by itself. You need to open it in a browser to make it work as intended.
Node.js works similarly to a browser’s runtime engine. It lets you deploy JavaScript code outside the browser, which has various advantages.
To answer your question—yes, if you host Node, you’ll most likely use it for server-side scripting. However, it has other applications. Hell, you can even use Node.js to program a robot.