A browser is some software running on your (the client) computer, enabling you to interact with the server. Common browsers are Netscape's Navigator, Microsoft's Internet Explorer, and also the Norwegian Opera browser. (See a webpage comparing several browsers)
Except communicating with the server, the browser also does a lot on your computer.
Sometimes the page contains data readable only with some application software (like Adobes pdf format), or even contains programs that can only run with some interpreter. These programs able to read those formats, or able to run the programs, are called plug-ins. (Here is a web page describing some plug-ins.)
(Interactive) programs that should run on the browser's computer are sent together with the webpage and executed.