In most common use, a server is a physical computer (a computer hardware system) dedicated to run one or more services (as a host), to serve the needs of the users of other computers on a network. Depending on the computing service that it offers it could be a database server, file server, mail server, print server, web server, gaming server, or some other kind of server.
In the context of client-server architecture, a server is a computer program running to serve the requests of other programs, the "clients". Thus, the server performs some computational task on behalf of "clients." The clients either run on the same computer, or they connect through the network.
Servers often provide essential services across a network, either to private users inside a large organization or to public users via the Internet.