What is the real purpose of installing composer and node.js, and the npm install?
composer is the dependency manager for php laravel framework. Look at this link for more infomation on this: https://www.tutorialspoint.com/laravel/laravel_installation.htm
Node js : like @ceejayoz said, it is not mandatory for laravel but may be needed to hook up some external tools.
If by non install you meant npm install, npm is the package manager for node js (npm stands for nodejs package manager). This is a tool that lets you install several packages that work with nodejs. According to the npm website, npm lets you discover and re-use over 470,000 free code packages in the npm Registry.