In the 90s, Microsoft violated antitrust law in its actions against Netscape, but not in the way most people realize. Microsoft created Internet Explorer to destroy Netscape as a company. Even in the very early days of Navigator, people were saying that the Web would be the new operating system, and that apps would move from the filesystem to the network. Microsoft knew that if that happened, nobody would ever buy Microsoft Word, or any of their other crappy products, because they owed the overwhelming majority of their sales to user lock-in through the operating system.
Another company which noticed all this going down was Google. Hence Google Docs. I have two useful spreadsheets on my iPad, zero on either one of my two computers, and at least 20 or 30 on Google Docs. Google liked the idea of moving applications off the desktop and onto the Web, since the Web mostly belongs to Google. (Of course, Microsoft hated it, because the desktop mostly belongs to Microsoft.)
Google championed the idea of lightweight Web apps in the days before Ajax was even a term, along with a whole community of small, scrappy entrepreneurial companies, of which 37Signals and Adaptive Path are the most famous examples. The modern ecosystem of Gmail, GitHub, Google Docs, Harvest, Shopify, Lighthouse, Campfire, etc., came from a rethinking of Web apps that was somewhat radical at the time.
Where Microsoft saw a hypothetical future coming and worked their asses off to spoil the party - being evil, as usual - Apple looked at the new landscape and questioned their most basic assumption. If all the apps are simple and lightweight and in many cases just run in a Web browser, then you can make your computers a lot smaller and simpler too. I'm writing this blog post on an iPad with a Bluetooth Apple keyboard. I do some spreadsheets on it, plenty of writing, and some music-making which is as good as the music-making on my laptop. I would never dream of editing video on this tiny sliver of a box, and its best SSH client still isn't ready for prime time in my opinion, but I use "dawn of Ajax"-era apps the most (e.g., Gmail, this blog) and for that, you don't really need a computer. If those apps hadn't changed what we expect from software, though, the iPhone would have been less useful, and the iPad might have never happened.