A “server” is any program that accepts commands or requests from another program and responds with data or actions.
A web server is, in essence, sent a line of text that asks for a file from a specific directory, and it sends that back.
The Client is the program than makes the requests and uses the replies.
eg. Search this on Google:
“simple web server tiny.c”
You should get a result from the site cs.cmu.edu – that page has the C source for a minimal but working web server. All in one not too large page.
A database server takes a request for a data record.
An email server takes command to list the emails a user has and send whichever are requested; plus talking to other email servers as either client or server, depending which starts the connection.
A “server” computer is just one that is dedicated to running some server programs.