NPM buys you automatic dependency resolution, a one-step process to update all your installed libraries to their latest versions, and the ability to pin some libraries to specific versions if you want/need to.
Some of these things you can get other ways -- libraries you load from a CDN will generally come with any critical dependencies already bundled in, for instance. But those solutions have their own problems; loading from a CDN means your app's performance is now tied to the performance of a system you don't have control over, and if the file on the CDN ever gets hacked, you're screwed. Managing your libraries with NPM lets you keep control over these sorts of things.
Some of these things you can get other ways -- libraries you load from a CDN will generally come with any critical dependencies already bundled in, for instance. But those solutions have their own problems; loading from a CDN means your app's performance is now tied to the performance of a system you don't have control over, and if the file on the CDN ever gets hacked, you're screwed. Managing your libraries with NPM lets you keep control over these sorts of things.