I'll try to cover a bit more of the pre-iphone evolution of flash-like alternatives.
Quite a long time ago now there became an increased desire for having stuff in a browser that is more like an app than a collection of pages. This wasnt new, and had been done in all sorts of ways with java and (usually really badly) flash before. But with a reasonable choice of browsers, faster computers & graphics, people started to do it more and more with javascript. Things like AJAX became popular methods for squirting data from server to client without refreshing the whole page, incentives were there to improve javascript and all sorts of people knocked up interesting toolkits etc. For example some people started coming up with a variety of animated page elements that served the user experience on websites well, and some of the ways they were having to use javascript etc to glue this functionality together was clunky. People started wanking about Web 2.0 because it felt like some kind of milestone had been reached. As several companies were busy steadily improving their browsers anyway, they looked at this stuff and started introducing additional stuff to their browsers, for example by adding their own stuff to CSS to enable animation to be handled by the browser rather than having to do it in javascript. And they made their javascript engines faster.
Apple were certainly into this, and one reason became clear later when the iPhone appeared. As there was originally no app store or other method for 3rd parties to write apps for the iphone, all of the initial focus was on webapps, much to the understandable disgust of those who wanted to write apps that were not well suited to javascript webapps. Anyway, we know the picture soon changed but at that early stage Apple were easily able to incorporate work already done with webkit to include a variety of CSS elements that enabled hardware-accelerated animation, thus ensuring the webapps had approximately the same smooth UI feel as the rest of the device.
So thats one element, which is part of what some people mean when they say HTML5, although much of this is really more like CSS3 & javascript. If memory serves me correctly when HTML5 first started to emerge it was quite likely that many were more interested in what it offered in terms of semantic tags and being able to get away from various flaws or limitations of HTML4 & XHTML, and the fact things in the past had ended up being divided into 2 with XHTML as well as HTML.
edit - this post was stupidly long, even by my standards, so I have chopped out the paragraphs of waffle about video, I'll save that for another time.