A component is software or script that has been written to assit your website...joomla has hundreds of thousands of components that have been made to work with joomla...most are free. The joomla community works off donations with the hope that the software written for your purpose assists you so much that you want to contribute and become apart of the community.

Components normally come with either a plugin and a module to that the component can be placed in different areas of your website...the plugin is in my opinion is the real power...this enables the component to operate with the website.