This is enormous news. I could see a scenario where, in ~5 years, WebAssembly could provide an alternative to having to develop apps with HTML for the web, Swift for iOS, and Java for Android. Instead, you could build browser-based apps that actually delivered native performance, even for CPU- and GPU-intensive tasks.
Of course, there would still be UI differences required between the 3 platforms, but you would no longer need 3 separate development teams.
This was also what Java applets were meant to deliver – I remember running some pretty great Java Applet-based games back in the day.
But Java ran as an embed, not a browser-level feature, and was much slower to load than Flash (which came to offer much of the same functionality in an easy-to-use IDE).
I can already imagine a minimal java VM (just transforming bytecode to wasm instead of JITing to machine code) inside browsers, thus allowing java (or any of the other JVM languages) running in the backend and frontend.
Google previewed some Android to chrome app compiler a while ago - can't remember the details. I imagine it would be a pretty good starting point for such a project instead of a full vm.
The creator of Swift was a creator of LLVM. Once the language has been open-sourced, it won't be long before people are compiling it to WebAssembly and trying to use it to replace JavaScript. He might not be too upset.
Of course, there would still be UI differences required between the 3 platforms, but you would no longer need 3 separate development teams.