Honestly? NodeChef is cheaper and does the same exact thing as Galaxy. Also, Galaxy’s APM is proprietary to MDG, I believe, whereas it looks like NodeChef uses the excellent and recently open-source Kadira for performance monitoring.
If you want to support MDG by having a Galaxy subscription, that’s awesome, but if you’re on the fence, read up on both. The choice should be pretty obvious.
As for why it’s better than a “conventional” deployment, it basically saves you all the overhead, hassle, and cost of setting up and maintaining your own server and DB environment, lets you focus on building your apps. I know because I manage my entire project deployment, including all my servers, DBs, and versioning locally.
I think as a student it could be an incredible learning experience for you to do that as well, but if you’re trying to build and host an app to the public to make money or whatever you should definitely just leave it to a hosting provider like Galaxy, NodeChef, DigitalOcean, or AWS, etc.