What is a server?

Servers are computer programs that receive requests from other programs, the clients and send back a response e.g share data, information or hardware and software resources.

...and what is a server in plain English?

A server is a computer program. Its job is to send and receive data.

Let's take a website for example. A website is just a collection of HTML and CSS files, images, maybe some javascript files. When you type a website address in your browser's address bar, the browser (client) sends a request to the server that lives at that address. The browser asks the server to give it the files it needs to display the website properly.