In the real world, businesses have clients. In the computer world, servers have clients. The "client-server" architecture is common in both local and wide area networks. For example, if an office has a server that stores the company's database on it, the other computers in the office that can access the datbase are "clients" of the server.
On a larger scale, when you access your e-mail from a mail server on the Internet, your computer acts as the client that connects to the mail server. The term "client software" is used to refer to the software that acts as the interface between the client computer and the server. For example, if you use Microsoft Outlook to check your e-mail, Outlook is your "e-mail client software" that allows you to send and receive messages from the server. Isn't exciting how it all works?