There are probably some good resources that you can tap into for an explanation of what an auto-event variable (AEV) is (for example https://www.simoahava.com/analytics/auto-event-tracking-google-tag-manager). The way an AEV is described in that article is that it is
[variable] that can be used to refer to, for example, the DOM element where a click occurred.
The key phrase here is "where a click occurred". My own definition would be:
a variable that corresponds to the last element that was last interacted with.
If you want set up a trigger for a particular tag based on the element that was last clicked, and there are attributes of that element that you need for your trigger that might not, for some reason, be available through the Click or Link Click listener, then you would use an AEV. It gives you the ability to get a data-attribute, a class, ID, etc.
Element class can refer to the broader set of HTML elements that have a particular class, and
Click class refers to the latest element that was interacted with (or clicked). By setting a trigger to include an AEV where it has an
Element class of some value, it will fire the tag whenever ANY element with the particular element class is clicked. Now that I'm typing it out, it's a bit more confusing. I'll likely come back to this to revise it, but I hope it helps a bit.