In information technology, the term is used quite broadly. However, it can be simply defined as any computer that provides data to another computer or other computers. This can be done over the internet, a wide area network (WAN), or a local area network (LAN). Sounds simple enough, but this is where it gets a bit more complex.
There are file servers, mail servers, and web servers. Each type of server utilizes software specifically for the service that they provide: a file server will use a program (like Samba) to share files over a network, a mail server will depend on programs (like Exim or iMail) that allow emails to be sent and received, and a web server might run Apache HTTP or Microsoft IIS, which allow internet and website access. There are additional types of servers—database, gaming, and application servers—that use different programs to accomplish their specific tasks.
While the software involved will be specific to servers, the hardware will not. Any regular desktop computer can be turned into a server by installing the proper software. Example: a computer on a home network can be designated as a print and/or a file server. Usually, however, businesses use dedicated, rack-mounted hardware designed just for servers and their functionality.
Servers typically function using a client-server architecture in which servers run programs to satisfy requests from other programs—the clients. In a client/server model of programming, the server is the program that receives and satisfies requests from the client programs on the same network. Clients usually connect using the network, but can also be run from the same computer as the server. The alternative to client-server is peer-to-peer networking, which allows all computers to function as either a client or a server, depending on what is needed. Client-server architecture is the most common, however, since it’s used for websites and email services. Windows and Linux operating systems are designed with this architecture in mind.
Really, understanding a server is just the tip of the iceberg. There are a ton of other technologies and terms to understand before a server will make perfect sense. But, for broad-strokes purposes: any computerized process that sends a resource to be processed by one or more clients can be called a server.