Joomla Plugins do a couple of different things for a website. They can provide specific functions, such as enabling a web designer to include code within an article or module, or providing a method of easily tracking statistics for Google Analytics. They can also provide access to OTHER plugins so that other developers can interact with them in meaningful ways.
Plugins are sometimes harder to understand because you don't always see what they do or interact with them in terms of an editor or form, but any time you've clicked the button below your editor to insert a Readmore line, you've interacted with a plugin. And if you've inserted image gallery code in an article's contents, you've used a third party developer's plugin.
Sometimes plugins come as a separate installation, but often they are also bundled in a package with a larger extension. For instance, some eCommerce extensions include plugins that allow web designers to include single products directly in a Joomla Article.
{jb_purplebox} To learn more about how plugins fit into the Joomla Extensions heirarchy, watch lesson 12 of our free Joomla tutorial course - The Basics. {/jb_purplebox}