Web apps have so much more the advantage than desktop apps in many ways. Giving these same apps the power and performance of a desktop app makes technologies that enable this power very interesting. The emergence of JS frameworks that enable single page apps is an area of high interest to me.
Single page apps (SPAs) are ones where only the content that changes is sent from the server to the client browser after the initial page load. In web and mobile apps, this means headers, footers, menus and more do not have to be sent to the client over and over again. When implemented correctly, SPAs are significantly faster than apps that do a complete screen refresh every time the user goes to a new screen or feature.
Gmail and Google Maps were probably the first two web apps that popularized the SPA. Many other web apps use this approach, such as Facebook, Zendesk and Flickr.
High performing apps are becoming even more important for mobile apps that require a server component. The performance over mobile connections can be an order of magnitude faster with an SPA. Users' tolerance for slow performance apps is growing lower and lower by the day.
SPAs are not for every application, but I believe they are for most. And SPAs can be used for websites as well.
I personally believe SPAs are the future of web and mobile apps. They enable these apps to perform and appear much more like desktop apps. I believe users will demand higher performance, especially for applications that live online in the future.