Elements are application instances, for example an image, a menu, a text element, you name it. On the end-user level, elements are the atomic building blocks of Boomla. (They map to a file on the Boomla Filesystem.)
Elements can be composed into, well, components. The benefit of working with components is that it is a higher level of abstraction, it lets you build websites with higher level building blocks. It's also great to provide you with lots of ideas, so that you can have some creative inspiration. The truth is, we are better at modifying things than comping up with novel compositions ourselves...
You can find a list of all elements in the Boomla UI kit - just click around. You will find lots of test-cases there as the site is also used for development.
This UI kit is installed as a package onto every template (..that uses it). Once you clone a template, you can open the New Panel to see all the available components.