Servers / personal cloud solutions – nowadays data often lives on the internet. If Dropbox, One Drive, and the other cloud alternatives feel unsafe or too costly for your data needs, mini-computers can help you out.
As a bonus, you can also host your site on such a machine, until it becomes hugely popular, in which case you may seek a more scalable solution. Gaming – unless you are a professional gamer, requiring a supercomputer for your hobby, a mini-computer can do the trick.