A server is a computer designed to process requests and deliver data to other (client) computers over a local network or the internet.
Not all servers serve websites: everything downloaded over the internet has to come from a server somewhere, like the npm packages you download when setting up a NodeJS app, or the data fed into your weather app on your phone. A sever that serves webpages over HTTP is not surprisingly called a web server.
You can run a static web server as a standalone program using software like Apache or NginX. If you need to have server-side business logic, you’ll probably write your own server app using a backend web framework like NodeJS, Python’s Django or Ruby on Rails.
Every web app uses a server. Any video game, mobile or desktop app that wants to store any information centrally will need a server as well. Understanding how the internet works and how to set up and run servers is not optional.
The MDN docs are a good place to start learning the ropes of server-side programming.