1. A program which provides some service to other (client) programs. The connection between client and server is normally by means of message passing, often over a network, and uses some protocol to encode the client's requests and the server's responses. The server may run continuously (as a daemon), waiting for requests to arrive or it may be invoked by some higher level daemon which controls a number of specific servers (inetd on Unix).
There are many servers associated with the Internet, such as those for HTTP, Network File System, Network Information Service (NIS), Domain Name System (DNS), FTP, news, finger, Network Time Protocol. On Unix, a long list can be found in /etc/services or in the NIS database "services". See client-server.
2. A computer which provides some service for other computers connected to it via a network. The most common example is a file server which has a local disk and services requests from remote clients to read and write files on that disk, often using Sun's Network File System (NFS) protocol or Novell Netware on PCs. Another common example is a web server.