"Cascading" in this context means that because more than one stylesheet declaration could apply to a particular piece of HTML, there has to be a known way of determining which specific stylesheet rule applies to which piece of HTML.
The rule used is chosen by cascading down from the more general declarations to the specific rule required. The most specific declaration is chosen.
When I teach CSS, I always tell the students that "cascading style sheets" means something like "fighting style sheets".
One rule tells your H3 tag to be red, another rule tells it to be green -- the rules are contradicting each other, who will win!? Stylesheet deathmatch!
OK maybe that's a slight exaggeration, but it's far more amenable to non-code, non-programming people who are just starting out than any notion of a cascade, or inheritance.
I do of course make sure to tell them that it's not a problem for the style sheets to be fighting each other, that's the way the language was designed.
Håkon Wium Lie (CSS co-creator) defines "cascade" in his PHD-thesis on CSS as "The process of combining several style sheets and resolving conflicts between them" https://www.wiumlie.no/2006/phd/
The following article answers your question perfectly.
It's the order in which properties are applied on a particular element(s).
http://www.blooberry.com/indexdot/css/topics/cascade.htm
You have to think of it from the outside in. If you have a rule that that is on the body tag it will "cascade" through every child tag. If you put a rule on any tag inside the body it will adopt that rule, and so on. So the rule cascades through all the content unless interrupted by a rule from an embedded tag.
You can treat the CSS processing as a waterfall contains several cascades. Here are those cascades from top to bottom in order: (The lower can override the same property in the higher.)
See more in the spec
The cascading is to pick the right value from multiple origins. But it's different from sorting. Only something not in order need we to sort. But in CSS these origins have fixed precedence. And thus the pseudo-code might look like the follows:
From the pseudo-code you can see it quite looks like a waterfall of several cascades.
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