In the "inverted pyramid" the most important information (which should come first) is represented by the base, which is the biggest part of the pyramid and holds up the rest of the pyramid. In a sense, it is the foundation, so you have to "get it right".
The analogy is "base = big = foundational = important"
Personally I think that's confusing, because you just as easily say the tip of the pyramid should represent the most important information, which should be conveyed concisely and without extraneous detail or background.
In that case the analogy would be, "tip = concise = main point = important"
That is confusing. In my mind, the tip of the pyramid is the smallest part of the pyramid, just like the brief overview at the beginning of the post is the smallest part. The base of the pyramid is the biggest part of they pyramid, so that is the bulk of the post where it goes into detail.
The "inverted pyramid" first described a visual pyramid, not a conceptual pyramid. I found an 1887 article in Time magazine on journalism, describing the inverted pyramid structure.
Specifically, the top of a newspaper article (the display, summarizing the article) consisted of not just the title, but multiple lines of different sizes. First, the title in large capitals. Next, a line of small capitals. Finally, three, four, or more rows of smaller type arranged in the form of an inverted pyramid.
That is, the lines in the heading got progressively shorter, making a visual inverted pyramid, with the most important information first.
Later, the "inverted pyramid" term described the structure of the entire article with the most important parts first, but the metaphor does seem backward.
It's funny because from that diagram I really don't see any particular relationship between the shape and its content. You could draw a regular pyramid with three segments and write the same labels on it and it would make just as much sense to me.
If anything a regular pyramid makes more sense to me: you want the smallest/narrowest useful description at the top and then you gradually expand on it as you go down, providing more (wider) context and detail for the key information.
Edit: Of course, it's a widely used term and good to understand in that context; the Wikipedia link is useful.
I think it's about laying foundations at the beginning, not the length of the text at the beginning. The first sentence/paragraph is the foundation of everything beneath it, whereas the base of a normal pyramid is the foundation of everything above it.
