A server computer (often just called server) is a computer system that has been designated for running a specific server application or applications. While a server application is "an application program that accepts connections in order to service requests by sending back responses."
A server application can run on the same computer as the client application using it, or they can connect through a computer network. Examples include file server, database server, backup server, print server, mail server, web server, FTP server, application server, VPN server, DHCP server, DNS server, WINS server, logon server, security server, domain controller, backup domain controller, proxy server, firewall, etc.