Plugins are described on this thread:
Introduction to plugins
Basically it is a way for end user developers to extend the functionality in Calibre, creating something that you can download and install. Such as giving you a menu item that lets you Find Duplicate books in your library, or a metadata plugin that pulls series information and covers from Goodreads and many more.
Plugboards on the other hand are just a specific configuration feature in standard Calibre which are related to changing certain information (metadata) contained about a book when you send it to your device. A common usage is to change the title of your book to prefix it with a series name if it exists, so that when you sort your books by title they are listed in series order. The sticky covering plugboards is
here.