Anything that occurs on the client in a client-server relationship. For example, CSS is clientside because it's used by the browser. PHP is serverside (the opposite of clientside) because it's used by the server.
Cascading StyleSheets is a webdesign language used as an extension of XHTML. CSS is meant to define the appearance of a website, while it's structure is defined by HTML. It is thus called because it uses stylesheets, external files whose properties are applied to the relevent sections of a website. They are 'cascading' because of the CSS rule of specificity.
CSS allows us to apply standard formatting to an entire website. We could, say, apply the selector "title" to every title, and then define it as bold in the external stylesheet. In this way, changing a single line in a single file will update the entire website.