For a very long time, if we wanted to make an application that worked in different browsers (desktop or mobile), we would need to write a bunch of browser/device specific CSS to make everything look alike. This was because browsers in the past never really followed a consistent standard.
I remember a few years back when we had to support IE6. Our sites looked great in Chrome and Firefox, pretty good in IE7 as well, but it was completely mangled in IE6. Trying to override the correct CSS rules and re-align everything could be a project on its own. There were a bunch of other problems that we faced with older browsers such as audio and video compatibility, but that's another topic entirely.
With HTML5, we have standards that help manage and maintain consistent content throughout multiple platforms. What does this mean? - My short answer would be, increased productivity, ease of maintenance and smaller team sizes. Also, HTML5 doesn't just mean new and improved tag elements, it also leverages CSS3 and JS.
I say increased productivity because HTML5 really makes things a lot easier to do. It also provides much more functionality than it used to. As developers, we wouldn't need to look into different plugins for animations or different ways to implement input validation or even geolocation. CSS3 is a very powerful tool for creating animations, transitions and various fading effects. The input tag lets you differentiate between email, password, range, even color in some browsers. More are listed on W3Schools.
I also said it's easier to maintain. That's because as time goes by, the standards will only solidify. There will probably be new or modified ways of doing things later on, but the core functionality will remain the same. This makes it a lot easier for new developers joining the team to pick up the work.
Lastly, smaller teams. This may or may not be true in some cases. But relative to the past, I believe it would require less people to develop a cross-platform application. That's because it would require less effort to maintain a consistent look and feel throughout different browsers and devices. Another great thing about CSS3 is the ability to create Responsive Designs a lot easier. Responsive design is what makes a web application like Kobo look so good going from desktop, to iPad, to iPhone/iPod.
With the advances of HTML5, I believe we have the tools to produce powerful cross-platform applications with a lot less effort than before. HTML5 is really a beast of a technology and topic. I've just highlighted a few of the areas that really popped out at me. There a many more reasons and various different topics we will discuss later on. Feel free to leave a comment!