Although it may be apocryphal, the story goes that the pyramid method was invented when reporters started using the telegraph to transmit their stories across the country to their editors. Prior to this, most articles where written much like today's school essays or technical reports, that is, in a deductive style with the conclusion at the end. But reporters quickly discovered that the telegraph was an unreliable transmission mechanism. Not only was the physical connection unreliable, but also they could easily be bumped off the line if someone more important, like the military, wanted their place. A half-transmitted article with the conclusion at the end was useless ("So, Custer was in an exciting battle, but did he win or lose?").
The reporters quickly adapted their writing style so that each article started with the most important details. This new format meant that if their transmission was cut short, then their editor still had the most valuable article possible. It also meant that the reporters kept their jobs and their incomes; what's the point of having a roaming reporter if he can't reliably deliver good copy?
Although the inverted pyramid approach has also been used for decades within software development to reliably deliver good software on time, despite the extreme uncertainty faced by most projects, it's only become well known within commercial software development with the growing use and awareness of the agile approaches such as Scrum and Extreme Programming. We don't refer to these approaches as the inverted pyramid. We use other names like evolutionary, iterative, incremental, or spiral, but the principles are the same: prioritize the features (or paragraphs, as in a story), deliver them so that our customers (the readers and editors) can consume them, and then repeat the process.
One of the reasons why the inverted pyramid approach succeeded is that it not only helped the journalists keep their jobs and made the articles more readable but also made the editors' jobs much easier, too. They would edit each article and then shorten it according to how important they judged the story and how much space they had available. If the article was on the front page, it also ran the risk of being chopped down to accommodate late-breaking news. The inverted pyramid style gave them the flexibility to quickly resize the article as needed. It meant that they could meet their daily commitments of shipping a highly readable newspaper despite the fixed space available.
Similarly, when software projects use the inverted pyramid style, senior managers have far more flexibility to react to changes in their environments. If a new opportunity opens up in the marketplace, then they may choose to close down an active project to work on the new opportunity. Since the software on that project is currently the best it can possibly be and because it is currently useable, the investment is not lost. In fact, the customer has received the best possible software he could expect and the organization has invested its development budget in the most profitable way possible.
I'm going to finish this article with what, ironically, is probably the most important point. One of the key lessons we can learn from the inverted pyramid principle is that when reporters are writing their articles, they will easily spend eighty percent of their effort focusing on writing a strong first paragraph, also known as the lede. Once they've correctly written the lede, they say that the rest of the article almost writes itself.