Selfhosted

When talking about hardware, the physical computer itself, a "server" is commercial grade and designed to run under heavy loads for years on end with very high reliability. Error correcting RAM, redundant power supplies, room inside for huge processors, more airflow than a C-130 for cooling, etc.

On the software side, a "server" is just a computer that provides some service to users on a network. You very likely have one of those Wi-Fi router/ethernet switch things from the likes of Linksys or whatever, right? That is almost certainly acting as a DHCP server for you LAN, in that capacity it might handle kilobytes of data a day because dynamically assigning IP addresses on a household Wi-Fi network is not a very demanding task, so it'll do it on a tiny little ARM processor with a few MB of RAM. It probably also has a web server, which is how the "go to its IP address in your browser and get to your router settings page" works. It's serving a little website that most of the time gets absolutely zero traffic.

So, turning a desktop PC into a "server." The question is, what services will it provide? Desktop PCs are pretty good at mostly low traffic with bursts of intense work, so if they're going to sit still doing nothing while you're at work all day, and then maybe handle some file storage or media transcoding during the evenings while you're home, a PC will do that just fine, if you're okay paying the power bill of having a computer up and running all the time.

If you're hosting a website or a game server with a lot of active users around the clock, you might want to look into more professional hardware.