Anything can be a server really, including your toaster: https://laughingsquid.com/netbsd-toaster/
But typically, servers are built with more performant and reliable hardware in mind. The kinds of servers your PC or phone talk to when checking your email or watching a video are rack mounted and basically look like a pizza box 
And a rack can have dozens of these stack on top of one another, and a data center can have hundreds or thousands of racks.
But nothing is stopping you from treating your home PC as a server. The software is the same since the same kinds of chips are in both your PC and the rackmount servers (generally). Running Linux on your desktop/laptop can allow you to do normal computer stuff, AND also share files, host a personal blog, share a printer, run a bittorrent tracker, or a tor relay, or even your own email. Some of this is even possible in Windows versions that aren’t “Server”.
Even these boxes will allow a serial connection. You can just open a tty and you can treat it just like a PC… if you’re comfortable on the command line.