The short answer:

Client/server is a computational architecture that involves client processes
requesting service from server processes.

The long answer:

Client/server computing is the logical extension of modular programming.
Modular programming has as its fundamental assumption that separation of
a large piece of software into its constituent parts ("modules") creates
the possibility for easier development and better maintainability.
Client/server computing takes this a step farther by recognizing that
those modules need not all be executed within the same memory space.
With this architecture, the calling module becomes the "client" (that
which requests a service), and the called module becomes the "server"
(that which provides the service).

The logical extension of this is to have clients and servers running on
the appropriate hardware and software platforms for their functions.
For example, database management system servers running on platforms
specially designed and configured to perform queries, or file servers
running on platforms with special elements for managing files.

It is this latter perspective that has created the widely-believed myth
that client/server has something to do with PCs or Unix machines.