You may commonly see references to “clients,” “servers,” and from time to time, “user agents.” And while you may, correctly, guess that a server is something that serves up data, the other two terms aren't quite so obvious.
A client is something that connects to (works with) a server. For instance, an “e-mail program” may be referred to as an “e-mail client”. Another one you'll commonly hear about is an “FTP client”.
The term “user agent” has a similar meaning to client, but it's more extensive. It's a program a person uses, as an agent (it does the task for them), for some type of activity. One example would be a “web browser” as an “user agent” for viewing web pages (amongst other WWW functions that it might be able to do). You could call a web browser a client type of program as well, but seeing as a web browser is a bit more multifunctional than some other single purpose client programs, calling it a user agent may be a little more all-encompassing.
The use of terms, such as client, is for the purposes of clarity. Simply calling an FTP client, an “FTP program,” instead, is too vague. An FTP client is used, by the user, to transfer files. An FTP server is used, by a service provider, to provide access to files. They're both “programs” but they have two distinctly different, although related, functions, so they (rightly) have distinctly different titles.