What Is A Server?
Before we address what a computer server is, you need to know more generally what a server consists of.
A server is essentially any combination of hardware or software that provides some sort of service to a given client. This is obviously a very broad definition, encompassing a vast array of potential services, hardware/software combinations, and clients.
Even a single personal computer could fall under this definition, all of its operations consisting of a series of servers and clients operating in parallel (ex., “master-slave" relations in programming.) Or, on a macro level, the Internet, with vast arrays of computers functioning in server-client relationships to provide you with everything from instant messaging to the very web page you're reading now. Thus, understanding the concept of a server is critical to understanding the infrastructure basis for our high-tech world, one of hierarchal relationships in programming.
Such grand things being said, the term “server" has the connotation of specifically referring to either a single computer or a single array of computers which provide a software or hardware process for clients in a given network, either consisting of public Internet users or private network users. The service provided could be anything from a cloud computing-style application to a stored file.