A server is any computer - or piece of software - that provides a service, eg. data of some sort, to another program or computer.
Many people think they are a special type of machine, but that only really applies to the cases used on ones built to be stacked in racks for places that need many computers.
If you run a game with multi-player capability on your own machine, it's likely got a server section (that holds the overall map & player positions etc.) and a client section, the part with the graphics and controls.
Quite a lot of other routine programs also have client and server sections; for some purposes it is a more flexible approach to creating programs as allows things to be shared from the server part, either to different sections of a client on the same machine or to clients on different machines.
A dedicated server computer is one built specifically to provide data or services to other computers.
It's in principle still just a PC, whether in a conventional case or a rack mount case, but usually without a screen and keyboard as no one needs direct access to it, everything is done through a network connection.
They may also have extremely large amounts of disc (or SSD) storage - or be linked to dedicated storage systems - if they are intended to hold large amounts of data.
However, that's not essential to being a server.
eg. If you, like many people, have a shared storage device (NAS) or an old PC somewhere you just use to store music or video to use from other computers or phones over your home network, that's a dedicated server.