A server is a computer that “serves” or gives files or services to other users or computers in a network. An example would be a “web server” which gives web pages to users who request them. File servers work similarly. Print servers control the printing queue for a specific computer, so any computer on the network can use that printer. There are countless types of servers these days with so much network-oriented software out there.
In general, the term “server” applies to either the computer that does the serving or the software used on that computer that enables the serving.